If you're running Skyrim ok your PC can't be that bad!
I've just taken these off my list of Steam games, so there may be better games or ones you'd like more, but these are ones I've played and enjoy.
RPG:
The Witcher 2 (RPG with a lot of depth to the gameplay, story and world. Not finished it, but it features multiple storyline paths you can actively choose, as well as smaller choices throughout the game. The combat is fun and fluid, and the storyline is very good. You don't have to have played the first game either, though it helps with the lore.
Action:
Batman Arkham City (or the previous one, Arkham Asylum). I've just installed Arkham City, but I can tell you Arkham Asylum is a really fun action game. The combat is fun and looks great, but isn't too hard. Gameplay all round very good and the story, for a Batman game, isn't bad at all. Everything I've heard about Arkham City makes it sound like an improvement on the first.
Strategy:
The Total War series (I'd recommend any of these, Medieval 2: Kingdoms
has a fantastic selection of mods, and Shogun 2 is very good. The latest, Rome 2, has very mixed reviews and I've yet to play it. These are amongst my favourite ever games!)
FPS:
Metro Last Light (Really atmospheric shooter, the gameplay is good and the story is surprising strong for an FPS.)
Open world:
State of Decay (this one is something I picked up in the last Steam sale and I love it. Open world zombie survival sim, where you gather survivors, pick a base, scavenge for supplies and try to survive. Barely played in the story in it because the other aspects are so fun)
City builder:
Tropico 4 or 5. Fun game where you are put in the role of an island dictator, building a city, town or whatever. Lot of fun to play an evil oppressive dictator who doesn't allow elections and "makes people disappear" with your secret police. Lot of depth and humour to it. Haven't played 5 but I'm sure it's good.
Finally, a left field one that you may love or may hate,
FTL - Faster than Light, it's a game that doesn't look like much, you pick a ship, outfit it as you go along and explore a galaxy, in a 2D-ish map. You aren't playing this for graphics though, it's gameplay is really fun and the thing that engrosses you most is the fact that if you get blown up, it's gameover for that ship and you have to start again. Makes everything that bit more exciting!
That may be enough to investigate for you now, if I think of any favourites of mine I'll post them.
As ever, make sure that your computer has at least the minimum system requirements!