Here's a thread from a few days ago that suggests games to buy in the Amazon App Store.

Here the games that I have bought recently:

• Battleheart

• Zenonia 2

• Max Payne

• Bike Race

• Ravensword: Shadowlands

• Breach & Clear

• CLARC

• Scribblenauts

• Monument Valley

• Sonic the Hedgehog 2

• Minecraft Pocket Edition

I think the best way to search for games is with the following filters from inside the App Store > Games section:

Genre

• Action

• Adventure

• Arcade

• Board

• Casual

• Puzzles & Trivia

• Racing

• Role Playing

• Strategy

Device Type (up to you, I don't have a tablet though):

• Phone

Price

• > $0.01

Average Customer Review

• 3 stars and up

Here's a link to that search under those filters.

I also recommend looking at developer's pages of the games you have played and liked, or developers you have heard of. For example, these developers have created games for Amazon's App Store:

• Sega

• Ubisoft

• Rockstar

• Square Enix