What about a sandbox game? Sandbox games include GTA, Saints Row, Prototype, Infamous, etc. These usually aren't too cut-scene heavy, and offer a wide variety of game-play, and are incredibly immersive. I highly recommend Saints Row the Second, or Saints Row the Third (I haven't played number one).
I haven't played Thief, but it sounds to me like it's similar to Assassin's Creed. Look into that series, i think you'd dig it.