A Dark Room
http://www.ign.com/articles/2016/01/08/ign-free-game-of-the-month-a-dark-room
You can get this for free through IGN right now. I don't usually care about IOS games, but this is honestly one of the best I've played, up there with Plague Inc. I just sunk 2 hours into this game, and it was good enough that I went to the app store and ended up buying the prequel, The Ensign. You guys really should get this one since IGN is giving it for free. The $1 it usually is is also more than worth the buy.
It starts off small but don't let that discourage you. The game really opens up the more you play it.