One option is to use the ANSCA Corona SDK in combination with a third-party tool called Lime. The essence of the Corona SDK is that it abstracts Java (or, in the case of iOS, Objective-C) in favor of the meager and simple scripting language Lua, while Corona has an extensive set of game-oriented libraries. You can then opt for iOS or Android using essentially the same set of code. Thus, lime is simply a tool that works in conjunction with Corona to enable the integration of Tiled maps, either orthogonal or isometric. Although both formats are supported, support for standard orthogonal cards is more thorough. Corona can be freely used for internal and special distribution. When you are ready to distribute and sell your application, you pay ANSCA for an annual fee of $ 200. Lime accepts a one-time fee of about $ 50.
The second option is to use Cocos2D for Android. This will most likely give you a little more power and freedom, but will also be more technical in its implementation. Being open source, Cocos2D is clearly worthless. Ray Wenderlich has a great tutorial on how to make a tile based game using Cocos2D. It is assumed that you are creating for iOS, but this is as close as possible to the tutorial, since you are going to use Tiled and Cocos2D in tandem.