What genre games do you prefer? 3rd person or 1st person? What would you like to do in that game? Would you like to have levels and quests or to create your version of the game world where you can build and be aware of the weather conditions, diseases and other people attacking you or play in the main game world where you can gain levels and etc? Multiplayer or single-player?
my favourite mobile game still remain 'The room' and Zombies. These two games are mind blowing as they work my thinking and creative strategy as I'm a cop. Try them and see. Again, its a thing of choice.
My favorite game on the iOS is by far Hearthstone:Heroes of Warcraft. It is a single/multi-player real time game (unlike a lot of the fake “multi player” in other iOS games), and it being a card game fits perfectly with the touch controls. Also its free-to-play model is fair unlike that of Candy Crush or PvZ 2 for example.
I haven’t played it on an iPhone, but I played it a lot on my iPad.