I want to build a game with a concept similar to Ingress, where the playing field is overlaid on a real world map.

Where do I get the map data for an app like that and how (in a very high level explanation) do I integrate my own game objects into that map. My game objects also need to move in real time so having them as static marker-like objects on the map won't work.

I thought that I might be able to use Google maps but as far as I can see it would be impossible to create my own graphical style, like Ingress has done, with the official API provided by Google.

Any help would be appreciated.