Yo, EDF
The good news is that after all that, NERV (and Misato, somehow) is still mostly intact. The bad news is that NERV is still intact, so as much as I'd like to help you guys rebuild and kick ass, we Eva pilots are going to stay in Tokyo and defend it from Angels. Before you ask, I don't know why they always attack us specifically either. I think monsters have it in for Tokyo in general.
Anyway...good luck, all of you, I mean it. I know it'll be far too difficult to go on without me, but I have total confidence in you, and that should be enough, ja? Whenever anyone's in Tokyo, go ahead and drop by the apartment. Christ knows there's plenty of beer. This goes especially for you, Nagare - I'm not going to let my training slide just because you got blown up. Send me the address of your dojo or something.
That's about it. When you get back on your feet, hassle NERV for an alliance deal again; I liked working with you guys.
~Tschüss!
From a strictly goal-oriented perspective, Asuka's next year is extremely boring, to the point where she complains loudly and frequently about being stuck in Japan for no reason - in the intervening period, only a single Angel attacks, and the Evangelions aren't even sortied against it. There was one...incident...with a certain American girl that Asuka has vowed to never speak of again, but other than that, as a giant robot pilot, Asuka's next year consists entirely of training, simulations, and testing. Naturally, that's not all there is to it, though - someone as aggressively energetic as Asuka can't just sit around.
Well, not for very long, anyway. Asuka, if given the opportunity, continues her training in Ryouma's batshit-school kung fu, as well as looking into something Katina gave her an idea for. While she already thinks of herself as the leader of the Evangelion team (which is one step above considering Shinji and Rei her backup/sidekicks at least), she realizes that there are formalities that will make them have to listen to her, so she goes through those to become an official "squad captain" - officially equal to a 2nd Lieutenant, so all the bridge bunnies still outrank her, but hey, it's something.
Work aside, Asuka spends most of her time at school, and hanging out with Shinji and even Rei to a greater extent than you'd think. In spite of her various reasons to not like spending time with either of them, well, they're the only other Evangelion pilots in the world, you know? Besides, she doesn't like hanging out with anybody, at least not in this stupid country. Might as well be people she has something in common with. She also passes the time with various hobbies, like teaching Shinji German (enough so he can understand when she swears at him, at least), taking care of Yamato's stupid pet bird to keep it from wrecking the apartment worse than it usually is, and even experimenting with cooking...this turned out poorly enough that she still makes Shinji do it most of the time, though.
By the time a year passed, a very dangerous thing results from this - a very bored sixteen-year-old Asuka with added authority who's actually somewhat getting along with her teammates. And really, really, really wanting to deploy and kill a monster, already, Mein Gott.