I'd probably just go with Bioshock Infinite, pretty good game. I still prefer the original, but Infinite is still good. It is of course very linear, story-driven, with virtually no "exploration" (doesn't need to offer any, since it is so heavily scripted, in the veins of Half-Life for example).
Skyrim is already pretty good by default (without any mods, or anything added to it) but to make it truly shine you'll spend way too much time tinkering with mods left and right, textures, etc. You might even get "lost" into modding and will never be able to finish it since you'll always look around for new ones, start new games to try different mods combinations, or always having to check for new mod versions. I've given to that for years with Oblivion and Fallout 3 (and Skyrim although to a lesser extent since I already started to get burnt with Skyrim modding after two months). It's almost a "risk". You'd have to force yourself to either 1) simply play the game vanilla, by default, from start to finish or 2) look around for the recommended "essential" mods (then again, you'll become curious and you WILL look around for more, believe me, that's when the potential addiction-to-Skyrim-with-mods issues start). In the end I think it might just end up being a chore. If you do have something like a year+ to dedicate to it then okay... go for it, but you've been warned.
As for New Vegas... well it's a decent game (without mods) but Bioshock Infinite is so superior that I just can't recommend Vegas over it. And anyway to me (and I know many will disagree, but I don't care) both Skyrim and Vegas feel way too dated by now (and yeah Infinite runs on UE3 but the art direction is superb, story is pretty cool, it's an "intelligent" game as I like to call those, it makes up for the fact that it runs on a very aging engine that's been milked to death in the gaming industry since the arrival of the PS3 and the 360 up to this day).
Yep, go with Bioshock Infinite in my opinion.