Since you're getting FF XIII, you obviously enjoy JRPGs, in which case I'd recommend Star Ocean: The Last Hope. It's not stellar, but it has a really fun battle system and some really hilarious and well done character interaction, and is a good game overall. I definitely enjoyed it (probably more than FF XIII, lol).

Another very good RPG for the 360 is Dragon Age: Origins. And then there is Elder Scrolls: Oblivion, and Fallout 3 and Fallout New Vegas. The last three are very open world, you travel in first person view, basically doing whatever you feel like. It's really great for exploration and immersion. Dragon Age isn't quite like that, and is more like a regular RPG, but with a really awesome and large world, good storyline, characters, the works.

There is also Mass Effect 1 and Mass Effect 2. 2 has more shooter elements and is harder, but Mass Effect 1 is more of an RPG, that just happens to use shooting as the primary means of fighting rather than swords and weapons of that nature. Plus, it has a good story, and is just a really well put together game. And Mass Effect can pretty much be played as a stand alone title, if you don't feel like continuing on to the second game.

Also, there is the sequel to Dragon Age: Origins, but I haven't played it, so I can't really comment on it very much.