I'm assuming you don't have a PC for games?
Mass Effect 1-3
Banjo Kazooie N&B
Ace Combat 6
Bioshock (I didn't like 2 that much but you might want to get it)
Assassin's Creed 2 (1 is not that good, if you like AC2 get Brotherhood and then Revelations)
Mirror's Edge is pretty fun and underrated
I hardly used my 360 when I was still at home though, so I'm sure I'm missing out on things.
I guess you could get Battlefield 3, but I dunno how good it is on consoles