I realise he's said about skyrim already, Still the best Single Player game thats been released for quite a while...
Current shortlist: Vanquish Alpha Protocol Tales of Vesperia Just Cause 2 Final Fantasy XIII Bulletstorm Beyond Good and Evil HD Scott Pilgrim vs. The World Braid Ms. Splosion Man
Brutal Legend Kameo - Elements of Power (launch title... don't expect super shiny graphics, but it's quite cool) Mirror's Edge Bulletstorm (Testo-shooter cheesecake) The Darkness (not particularly polished, but very, very cool) If you're like me (and at times it seems you are - notably when not liking Oblivion and GTA IV), then don't bother with Red Read Redemption... it's a bit like "GTA Horse".
IMO Mirror's edge was a good idea, thought the controls on the 360 were awful. Shame it didn't sell particularly well and got canned [as a series]
Like Zoon said, any of the Lego games are great. Some i've been playing\re-playing recently that i could recommend Batman: Arkham City Halo ODST Halo 3 Gears Of War 1 + 2 Fifa 11 Defence Grid (xbla) Storage Inc (xbla, simple puzzle type game, i love this game. 100 levels for for 240ms points) Here are some others Forza Motorsport 3 Braid Splosion Man
I would just get Arkham City and skip everything else. I haven't enjoyed a game this much for a looong time. There are some good deals on it if you shop around. p.s. I didn't like Oblivion either, and I don't like Skyrim. Beware of that game.