Firstly, I'm noticing a lot of people missing the part where the OP said he was playing on the 360. So many of the New Vegas recommendations; of which are based on the suggestion of getting certain mods to make the game better; are not only pointless but invalid.
Secondly, as much as I want to recommend Portal 2 (as it is a VASTLY superior game in almost every regard), I simply can't. Namely, for the same reason most people are pointlessly recommending New Vegas.
That reason? You're playing on the 360.
Why does that matter? Well, if you were on the PC I'd recommend Portal 2 in a heartbeat. This is because Portal 2 on PC just received the Perpetual Testing Initiative DLC. This DLC added both a superb, and surprisingly robust, in-game map maker/editor as well as a community share feature. As such, with this new edition, you'll end up getting a lot more play time out of Portal 2 than you would New Vegas.
However, seeing as the console builds can't really get this feature, I'd have to suggest New Vegas. Which is a shame, really. Portal 2 is a much better game.
(One quick caveat. I notice a lot of people saying "New Vegas over Portal 2 because you get more play time out of it." This is a load of crap. More play time =/= better play time. Just because a game has you playing for a longer period of time does NOT mean that it's play experience is automatically better. I hear the same thing with people claiming one story is better than another because it's longer and has a lot more dialog. Something that just doesn't make sense. Saying that it's a simple matter of quantity, though, DOES make sense. Which again, without the PTI DLC, is something Portal 2 doesn't have over New Vegas.)