I suggest getting Red Dead Redemption.
As much as I love Skyrim and as much time as I have put into it. Red Dead Redemption is one of my favorite games OF ALL TIME. The story and characters and gameplay and everything is almost perfect.
It is a game that just an average gamer can pick up without too much of a learning curve (whereas Skyrim has a pretty large one if you have never played a Bioware game before)
I also give Portal 2 a vote. One of my favorite games of the year, actually makes you think.
Skyrim was amazing. It's the deepest game I've ever seen and has some great replay value.
Saints row 3 is like gta, but not quite so serious. I wasn't a huge fan to start but the more I played, the more I chuckled about it.
Batman arkham city is awesome. Another open sandbox type game with a great storyline. Fighting can be repetetive but you can find new ways to beat guys.
Ace combat is exactly what you expect from the series.
I saw red dead redemption mentioned. GREAT game. Gta western. Exact same play.style and layout. Multiplayer gets boring quick.
Forza 4. If you can't play gran turismo, forza isn't bad at all.
Kinect sports 1 and 2 are so much fun, its worth buying a kinect for.
I still play rock band 3. Still one of the best party games ever made.
FYI, I have a nodded xbox so I play almost everything. If you have specific questions about a particular game, I can give you a better review.
And I play modern warfare 3 online all the time, even though I hate it because the multiplayer is better than battlefield 3.
Single player, modern warfare 3, battlefield 3 and gears of war 3 were all enjoyable but kinda short.
Red Dead Redemption and the enitire Assassin's Creed Series. If you go with Assassin's Creed, play them in order.
HALO Combat Evolved or Gears of War 3
Only 2 titles not mentioned from my 2011 GOTY Top 10 list was: Alice Madness Returns and LA Noire.
I wasn't a huge fan of LA Noire, actually. I mean it was a solid game, no doubt, but when there's GTA IV and Red Dead Redemption in the market...the competition is rather stiff.
-Portal 1 and 2 (brilliant games)
-Dark Souls (difficult but rewarding Action RPG, created some buzz but still extremely underrated)
I am a big fan of Pit Fall!