Till Nagel has a tutorial on using custom maps as backgrounds in Processing sketches. The solution uses TileMill, a map design environment which allows you to export a customised static map as an image for use in Processing. For advanced users, Till Nagel also describes the procedure for interactive tiled maps. That latter solution relies on an SQLite database and a JDBC library to connect to it.
I haven’t yet checked it out in depth, but it looks absolutely promising!