Yeah, I personally prefer story driven games in general. I don't mind combat, but an engaging story is what gets me - and all the better if game play and problem solving is creative.
I don't tend to do social gaming, but I can suggest you search things like "nonviolent mmos", "nonviolent mmorpg" and you'll probably find some lists, and try "social mmos" too. And you can always add in "free to play" or not depending on what turns up. And maybe check consider downloading Steam- it's great for PC gamers and has lots of indie games, inexpensive games, sales, AND you can use them to search for free-to-play stuff.
And if I come upon anything that seems like you might like it, I'll get back to you. ^^