The biggest pain I found living in London (that can be solved in a week) is bus lines visualization. I find almost impossible to visualize the route of a bus, much less to combine two routes to get to a point. The official site gives line number information from point to point, but no visualization. I don't know if the London transports has an API with real time information, but it could be cool to have all the buses diplayed in a map. This could be expanded to see delays, or other line issues.