Here's a list of good mobile games off the top of my head. None of these require in-app purchases if they even have them:
You Must Build a Boat,
The Executive,
Out There,
Monument Valley,
Hitman GO,
Lara Croft GO,
DEVICE 6,
The Room (and sequels),
Prune,
Lifeline (this one's great because it would only work in mobile),
Threes!
If you're looking for good mobile recommendations, I'd point you at http://toucharcade.com. They do iOS reviews, but a good chunk of the games also release for Android these days.
You Must Build a Boat, The Executive, Out There, Monument Valley, Hitman GO, Lara Croft GO, DEVICE 6, The Room (and sequels), Prune, Lifeline (this one's great because it would only work in mobile), Threes!
If you're looking for good mobile recommendations, I'd point you at http://toucharcade.com. They do iOS reviews, but a good chunk of the games also release for Android these days.