Corona SDK and Gideros are good 2D mobile frameworks.
Roblox as meme-y as it is provides an amazing developer environment.
I have used both bump.la and Hardon Collider with the Gideros 2d engine. I made a class which loads a tiled map and then creates bump and Hardon Collider shapes so it's not too hard to do. With Hardon Collider you just make your maps in tiled and add collision shapes.
Here's a link to the forum thread that contains all my ramblings on the subject. All the code provided is in Lua so some of it might be of use to you..
There's some basic SAT collision stuff in there too.
http://giderosmobile.com/forum/discussion/6353/collision-with-any-object/p1
Last I checked, the Gideros SDK was supposed to be going open source. It's a pretty great framework that will allow you to build for iOS, Android, Windows, and Mac osX. It also recently just had a successful kickstarter to fund a port to HTML5.
I remember liking it, but Löve2D may be superior at this point.
I'm currently learning Gideros, it went opensource 5 months ago (so now it's completely free) it exports to android and iOS and uses LUA as the language (I only know javascript)
I choose it because the games feel very fast and native and have heard only good things about LUA.
If you like it and you want we could learn together. Cheers!
I managed to integrate luaJIT in my Android Lua-based game Renabomb Vengeance ( trailer ) since both Gideros SDK and its plugins are now open-sourced. I'm uncertain with the stability but the game is obviously much smoother on my half-brick/half-phone device. I'm happy with the engine choice I made last Spring.
There is still few things I'd like to add to the game; notably, a real ending (with a boss?) and a "game run" mode. Someday.