The Silent Age from publisher House on Fire is a puzzle adventure game that moves back and forth from the present day to the 70s. You’ve-probably played games like these on the PC, but the features and interface are designed specifically for mobile devices.
Small Street is an “economy building” game, but rather than construct a tower where your residents can live in, this one will have you building a town and a strip mall. Created by Glu Games, it allows you to build shops, apartments and restaurants, populate them and find employment for your citizens.
2020 My Country is a city building game for the iOS and Android. Published by Game Insights, this is city building on a large scale. Unlike other city simulation games, 2020 My Country gives a large tract of land to start out, which is really nice so you can get going quickly. There is also a tutorial to guide you, great for newbies.