LilithSlave said:
I generally feel the same way. I'm getting really tired of combat.
I'm personally a big fan of puzzle-adventure games, and I
strongly recommend Machinarium; you can pick it up on Steam for pretty cheap. I think I heard you can buy it on PS3 now too, but I'm not sure. It's pretty tough, while also being fun, charming, and creepy-cute. Great soundtrack too.
One of my favorite games of all time is Riven, the second game in the Myst series. If you want a series with mind-twistingly hard puzzles, that also happens to be an old-school classic, check it out. The Steam versions are buggy as hell, though. (Also, I personally think the original Myst is one of the weakest games in the series. It looks bad and is kind of incoherent. Riven is fantastic, though, and Uru Live--free to play online!--is a fun romp.)
And you would probably enjoy Flower, though it tends to feel like a time-waster. Speaking of which, Journey is coming out soon, from the same people. You may want to look into it.
Oooh, Child of Eden and Rez are good ones too. You're technically shooting things in those games, but they're not representative of anything so it's hard to say they're violent. It feels more like hacking a computer program in a 90s movie, while making music.