The World Ends with You is possibly the single greatest game to come out of Squaresoft. Yes, I'm aware that the FF series was good, and Chronotrigger/cross were amazing in their own right, but it could possibly trump them, IMHO (hard to say... FF6 and Chronotrigger were pretty awesome, themselves - a tough call for sure). Don't do any research on the game (how the game's mechanics and world open up throughout gameplay is half the fun), and approach it with a pretty open mind, and you'll be in for quite an experience. The story is about 15 hours, but then the game really opens up sandbox-style. You can easily put in 70+ hours discovering just how much Square put into this gem.
It's not for everyone, though - the modern Japanese aesthetic is a big turn-off to many people, and the use of almost every hardware function for the DS (often simultaneously) can be daunting.
Oh yeah, and if you get it promise to remix some of the soundtrack with Jillian - it's sorely under-represented, and since it's almost all vocal music the both of you could really do some magic with it.
Let's see... If you don't have Bowser's Inside Story, that's pretty good, too (if a little short-lived). FFIV for the DS is quite well done - if you want to revisit that game with a serious difficulty overhaul then check it out (even if you already have the Advance version - they've made many significant changes to it to make it worth paying again while leaving the 'Spoony Bard' dialogue intact). If you have an RD card you could get the translation patch for the Saga 2 remake for the DS. Hey, they took out random battles, so it's certainly an improvement from the (stellar) original (unfortunately, unless you know Japanese then there isn't any other way to play this game).
The Megaman Zero Collection (may as well get that one, rather than collect all of them for the GBA) has some of the best MM gameplay I've seen, if you're into that kind of thing (and who isn't?). Be prepared for the ridiculous difficulty curve, though - every game is a notch or two above the normal 'Megaman' difficulty curve. The ZX series is... meh, alright, I guess, but I don't really recommend them.
Scribblenauts is a fun game. It just is. Seriously, what other game can you give God a chainsaw and have Him duke it out with Chthulu? (God wins, by the way)
Warioware (for the GBA, especially) is like crack. You'll get freakin' hooked for a good 4-6 hours before you can put it down.
Ogre Battle - Knights of Lotus would probably be up your alley, if you like strategy RPGs. It's Ogre Battle and it's a SRPG - you probably know what you're geting.
Those are my picks, anyway. In all seriousness, though, play TWEWY, even if not on this trip. You won't regret it.