What about Clash of Clans?? I'm super addicted to it. It's the only game I've ever had on my smartphone and tablet aside from Hill Climb Racing. Clash of Clans is a free and relatively straightforward strategy game. You absolutely don't have to spend any money on it to be great at the game. The only thing to spend money on, really, is extra Builders which will speed up your village's growth, and this is certainly not necessary.
The purpose of the game is to build up your own village using in-game resources: "Gold" and "Elixir" (and, later in the game, "Dark Elixir"). Additionally, you can raid other villages via the "Find a Match" menu and you can 'steal' a portion of their Gold and Elixir to spend on your own village.
I'd be interested to see your villages if you play

If so, there isn't much of a way to add friends on the game. The only "friends" are facebook friends if your account is linked, and soon they'll be adding Google+ friends.
However, if you do play: are you in a clan?? (that's the only way to look others up is if they're in a clan)
Would you be interested in making a future clan? (I'm presently in one but perhaps we could get one going if anyone else plays

Here's my village presently

http://i.imgur.com/HerEMm6.jpg