Good iOS games?

In view of a new phone, I'm trying to find some decent games for it. I'm a pretty casual gamer, so I'm totally happy with the platform (trying to suggest that I don't really care for a debate about it here). I'm a little bit worn out on Nintendo games right now, so I'm looking especially for games that have a good story, or are made by indie developers, free or paid.

I currently have installed/wishlisted (some of these on an iPad):

- Severed
- Old Man's Journey
- Card Thief
- This War of Mine
- Flower
- The Witness
- Beglitched
- Sunless Sea

Any suggestions along these lines would be greatly appreciated! (I know some of these are PC games too, but I don't have the hardware to run them on my laptop.)

i'm not sure if you're into any puzzle/puzzle-platform games, but monument valley (1 and 2) are pretty good games. recently, there was a port of fez to ios and it is very good too. they're all indie games and i think they're each $4.99, but well worth it.

Pixel Guns 3D