Brisbane City Council has maps of its bikeway network available on its website . It also has a separate ‘Active Travel’ set of maps that show more detail, but are only available in paper form. They are available at the Transport Information Centre, and can be requested online through the fix-o-gram service (under "Publications").
Bikely.com is a Google Maps-based site that lets you create, share and find individually mapped routes between particular locations.
Ride the City is an OpenStreetMap-based journey planner tailored for bicycles. Originally from New York City, it also has specific coverage of Brisbane.
OpenCycleMap is an OpenStreetMap-based site showing bicycle routes. Although still UK-oriented, it shows bike routes around the world.