When you read the words "zombie-themed base-builder," some of the more hilariously awful games on the Play Store come to mind, including this classic gem of wanton intellectual property theft. But don't close the tab just yet: Rebuild 3 is a zombie of a different off-green hue. First of all, it comes from developer Northway Games, which made such unique titles as Inredipede and Deep Under the Sky. Second, it's a premium $5 title with no in-app purchases, which is more than you can say for the vast majority of both builder and zombie games for Android.
And third, it's just a solid game overall. Rather than focusing on gathering as much currency as possible and building up structures and units, Rebuild is more about managing the scarce resources you have after the apocalypse. Most of that boils down to managing people, specifically your randomly-generated team of survivors, each of whom has unique skills that can be put to use restoring your city. Events like epidemics and zombie attacks will test your revitalized infrastructure, either in an open-ended, randomly-generated landscape or with a 30-mission campaign. A wide array of buildings, equipment, and research options can add considerable variety.
The game can progress either in real time or via turns, and the deeper strategic element comes into play when you meet other factions. (That would be the "Gangs" part of the title.) Different NPC groups control territory of their own, from former street gangs to the remnants of the government to closed-off school children. It doesn't hurt that the sprite-based graphics are unique and colorful, and don't resort to the played-out 8-bit style.
Rebuild 3 has been available on Steam for several months, where it's been earning very positive reviews from players. The mobile version works on Android 3.0 or higher, and at $5 it's only one third of the price of the desktop version. If that's still too expensive for you, you might want to wait for a Humble Bundle - the developer has taken part in the discounted bundles before.