Doing the actual con is essentially running all of those smaller events that you tested and perfected all at once / all in sequence over a limited amount of time. Having enough to do for everyone for the entire event is definitely a thing you'll be nervous about, but don't panic, because you already have enough practice at doing this.
It is still dangerous to go alone for the event itself! Make sure that you have all of your friends and fellow planners present to help deal with emergencies as they arise, to keep an eye on their designated sections, and to otherwise help wrangle and answer questions and enforce policies and otherwise be your trusted arms, eyes, and ears so you're not trying to do everything yourself. There needs to be enough people who are staff or trusted volunteers to make everything run smoothly.
Vendors and Artists
Many con experiences involve people who are selling things, whether good or commissions or fanworks for attendees. Being in a library space or being a library program may prohibit you from offering this at your con space, depending on the policies of your organization. Check with your lawyers about what, if any, commerce is allowed in your space.
If you can do commerce, you'll want explicit contracts spelled out about what can be sold, what can't, and how vendors need to behave in the space, when their times are to set up and take down, and so forth. There may also have to be information in the contract about how copyright works with the materials on offer and what can and can't be offered because of that. Check with your legal department, if you have one, about what has to be present.
Cosplay
cosplay (v.) Portmanteau of "costume play," generally refers to the act of dressing yourself up as a (favorite) character. It often involves makeup, fabrication of costume parts, and putting an outfit together intended to either faithfully replicate an original or transform it to work for a desired look or idea.
Cosplay is an involved art, and one of the things that cosplayers like to do is show off their work to an appreciative audience. In addition to the regular con showing-off, you can put on a runway show for all the interested cosplayers to show off their work. It can become a contest with judging, audience voting, and/or prizes as well, if desired, but that may discourage some people from entering if they feel their work isn't good enough compared to others. The fashion show idea is more inclusive and lower-pressure, so understand your audience and what kind of competitive nature they have.
Guest(s) of Honor
Like any other program, sometimes you can pull in some local or some big-name talent to appear at your event and have them talk and answer questions from the audience. So long as you're willing to work with their publicists, agents, and schedule, you can probably engage in talk with all sorts of people. Understand that a lot of them will charge money to come speak, and will have other requirements for their wrangling and lodging, so that will have to be put into your budget's accounting.
Panels and Workshops
A hyper-local and much cheaper alternative might be to have some of your knowledgeable teens and community members deliver panel programming about their fannish interests. There are a lot of topics that can be covered, some of which you may want to pre-screen for specific things or have the presentation delivered to you beforehand to make sure that it's appropriate for the right audiences.
Games
There's a lot of interest in gaming, so having some game programs at your con is a good way of getting people in the door. A way to make sure your program gets seen and read is to provide a game on the program itself, something like collecting stamps or visiting specific locations and programs, so that someone who doesn't quite know what to do has some suggestions and people who are sure they know what they want might try something outside of their comfort zones.
A low-cost way of getting games going at your con is to have some board games available for attendees to borrow and play with their friends. The library can be overseen by a few people even if there's a lot of games that are available. If you don't have a game collection already in place to use, you can potentially partner with local game stores to borrow their demonstration libraries (and possibly demonstration staff) in exchange for some promotion in your program or for a small fee. If you happen to know them (or can sign up to be part of them), people who are demonstrators for game companies can be brought out to show off things at your event as well. Board games are an easy way of having all-ages programming at an event.
With enough interest in your community, the popular collectible card game or hot competitive video game could have a tournament or other more formal event as part of the convention. You'll have to find people who are properly certified to judge, whether by the official sanctioning bodies or who have significant amounts of experience with that game and would know how to set up a tournament properly.
The things that are most important to consider for these kinds of events are time and money. Tournaments will take time and people to run properly, to the point where someone might have to be only in charge of running tournaments.
Furthermore, many of the most popular things are the kinds of games where more time or more money being invested will result in a better ability to play the game. Which can sometimes result in the tournament being full of hyper-competitive people who are looking to win and scare away anyone who might want to try the game or play it at a less intense level. Choosing a game where everyone has the same basic chance of winning and someone has to adapt their strategy to the players around them might be a better option than hosting tournaments for games that might be seen as more pay to win.
Alternately, you can decide not to have any competitive events at all, or host alongside the competitive events open gaming, where the point is to have fun, and possibly teach some games to people who haven't learned them, or for people to chill and play something neat with their friends. For smaller events, open gaming is probably the way to go for most things, as you won't draw enough people for the competitive types to feel like they're getting challenged at the games they love. Or which might be frustrating to have all of these good, but casual, players end up not having a chance against the highly competitive tournament one.
Video Programming
Especially for anime-themed cons, having shows to watch communally and bond over and sing along to or otherwise make commentary on is sometimes a big draw for people. You'll have to have someone there to monitor the room and make sure that people don't get too far out of the boundaries of the event with their commentary, but for the most part, the people coming to see the shows are doing so because they're already fans, or because they're interested in picking up new shows to become fans of.
If you plan on putting on video programming, make sure that your location has a Public Performance License that covers the things that you want to show. Nothing kills the mod more than having letters come for you alleging infringement of copyright for your friendly anime showings. If you don't have one that specifically covers what you want to show, some distributors like Crunchyroll or Funimation will grant public performance rights if you register a club with them and have an official presence.
Crafty things
A button maker is an instant hit for just about any kind of programming. It's pretty simple to use, once you get the hang of it, and the supplies for the button maker can be found in the thousands of pieces on various websites, ensuring that you'll have enough material on hand for your mini-con's attendees to put together whatever buttons they would like to keep with them after the con is done. You can help people who don't want to design their own button fronts by providing old withdrawn comic issues or templates of various (appropriate) memes and fandom sigils and badges so that people who want to proclaim their love for a particular faction or fandom will have material on hand to quickly stamp out their allegiance and attach it to their lanyards. Having a person on hand to help with difficulties and instruct the attendees on how to use the button maker is helpful, but it can be the same person assigned to the room for the other creative endeavours in the same room.
Giving attendees a big bucket of bricks and asking them to come up with whatever they would like is really good for some people who want to build with bricks (or who are curious to see if their Minecraft build ideas will translate well into the real world). For people who are less sure of their building creativity, having some materials on hand that offer step-by-step brick-building instructions will make the space good for everyone. Just be sure that things that fall off the table get picked up quickly and everything gets put back in the bucket, because bricks are often sturdier than flesh beings, and stepping on one is one of the definitions of pain.
If you have someone who is willing to stick close by to the hot irons that will be needed to fuse them, and who is willing to take the time that's needed to do the fusion correctly, Perler beads are excellent for people who want to create 8-bit-looking art and fuse it together into a complete item to take with them. It takes time and practice and being able to see the pixels to be able to help with Perler beads, as well as knowing how to operate an iron and make sure that it only melts the beads enough to get them to stick to each other, rather than to completely melt the project. Building with grids is also helpful for keeping the beads in place and at the right distances from each other to make the project work. Unlike brick-building, which ultimately gets taken apart at the end, Perler bead fusion produces something for an attendee to take home with them.
Doing makeup or facepaint is sometimes a hit, if you've got someone who can paint things they've never seen before or has a wide variety of possible paintings they can do, so this is a little more limited to people who you already know or can hire to do these things. If you get a person, though, with the right audience, this will be one of the most popular and long-lasting things that people remember about the con.
Other Possibilities
A photo or selfie booth is a neat thing for people to have to create mementos of their con experience. Make sure that you stuff the booth with a few different background ideas, frame ideas, or props for everyone to hold while they take the picture. With digital photography and cameras, people can take as many attempts as they want before getting it just perfectly, so we recommend people who have complex ideas or who are going to be perfectionists choose a time when the photo booth isn't in heavy usage to stage and take the pictures they're interested. You can also instant-print those pictures that you've taken through the use of entities like the Selphy printer, made by Canon, so there's an immediate memento available and printed.
If you don't have a booth to set up, you could get some official event photographers to document and take great shots of your event. Photography students, student journalists, and other amateurs looking for experience are great to recruit for this role. Make sure they understand what you want in shots and that everyone they're taking pictures of has given their permission to be photographed. (It is not too difficult to, say, have different colored attendee lanyards that indicate how willing someone is to be in photographs, even if you have a blanket permission to take pictures for the event.)
An alternate take, or in the same space as the photo booth, you can videotape your attendees and have them record a short video segment to be put together into a compilation at the end of the con. Have some prompt questions ready for your attendees to answer, with several general ones that make it possible for the attendees to take in whatever direction they would like for their answer. But make sure that they keep it short, so have questions that can theoretically be answered in less than a minute of recording. (The people who have to splice it all together at the end will thank you for keeping it short, especially if there are a lot of people who are participating in the video booth.
A thing to keep in mind about both of these ideas is that if you're going to be using the photos and videos for marketing purposes or releasing them to a greater audience than the attendees, you want to make sure that you've obtained permission from the participants to use their materials and likenesses for your purposes. This will probably involve parental permissions for minors, so have those forms on hand or make it exceedingly clear to the grownups who can give that permission that registering for your con means that this permission is granted for use. Since you may need a permission slip from a grownup to participate in the event all the same, stick the photography and videography language in that form so that the grownups know what's happening and have given written permission for it. Again, offer your attendees a way of indicating their personal preference of being photographed, even if you have that blanket permission obtained from their grownups. Uncomfortable attendees don't come back.
Any con of sufficient size needs a space where people can get away from it all. Chill spaces are essential to a good con experience, and should be placed as far away from the biggest noisemakers as possible, with rules specifically about how chill spaces are meant to be quiet, so conversations and other things should happen away from the space. Having a spot to decompress or otherwise just spend some time looking at a phone or other quiet activity, like coloring sheets or coloring murals, can be the difference between an awesome con experience and sensory overload for many of the attendees. Have a chill room.
Food is an awesome thing to have at your con, but make sure you have enough and that you space it out in such a way that you're not running on unwanted hard candies at the very end of the event. There will need to be someone who is monitoring the food and enforcing the food rules (almost certainly "Food does not leave the food room," for example.) Food can cause additional expense, but local business partnerships might mitigate some of that cost or provide the food at a discount to make it work within your budget, or they might be willing to take their food trucks / mobile kitchens to your event and have food available to the attendees (maybe, just maybe, at discount.) Especially with teenagers, we highly recommend food be present, but we know that sometimes it's not possible.