Definitely Arkham City.
I'm a massive Portal fan (as you can probably see by my avatar), and after playing Portal 2, I was confident that nothing for the rest of the year would even challenge Portal 2 for my GOTY. Currently, Arkham City has stolen my heart and soul. When the simple act of moving around in a game makes me gleeful and happy, I know I've found something special. If Skyrim is left out of the mix, then Arkham is certainly going to give you the most bang for your buck, as well- the amount of content in this game is astounding. You might want to consider trying Arkham Asylum first (also a fantastic game- it's better paced than City, but City is better in every other way), but if you really want to jump right into City, you can go right ahead.
A question of my own- I'm currently stuck with indecision about choosing between Skyrim and Assassin's Creed: Revelations to pick up in celebration after a killer chemistry exam tomorrow afternoon. This may seem easy to most of you, but take these factors into account:
1) I already have $10 down on Revelations
2) I still also have to 100% Arkham and play Super Mario 3D Land in what little free time I have, so I won't be 100% devoted to Skyrim.
3) AssCreed 2 is one of my favorite games of all time, but I was VERY disappointed by Brotherhood.