Ill give you 3 choices since 360 are expensive. But these are games i def fell in love with.
1. The elder scrolls: Oblivion
This game is amazing. Graphics are awsome in this game. Its almost in a way never ending. Im going to be honest i hated RPG'S until i played the elder scrolls series. Even if you dont like RPG'S i think this one will change your mind about them a bit. This game is addicting tho i warn you!
2. Ghost Recon Advanced Warfighter
Probly the best war based game out for the 360 right now. One of the funnest campaigns i have played in awhile for any game. Graphics are awsome especially on HI-DEF(omg amazing). Online is pretty cool but spawn killing is sort of an issue. But def a pick up.
3. Battle Feild 2: Modern combat
Another great war based game. Its basically the original xbox version with a few minor changes and better graphics. But if you havent played it at all the single player is also really good. There hotswaping feature is really cool. Online only has capture the flag and conquest but conquest is really fun and after you play it a few times you get addicted.
Those are my suggestions. You can take em or leave em. Enjoy your 360
