I would highly recommend a trip to the London Transport Museum. We visited for the first time a few weeks ago and happily spent a good few hours there. You can get a great feel for the history of transport and the history of London. I think the exhibitions clearly demonstrated how vital the transport network has been to the development of the City. I enjoyed the ‘Designology’ section of the Museum and seeing some of the old London Transport posters.
If you do visit, don’t forget to look up to spot these signs hanging from the roof:
The left photo here shows three bus Destination Roller Blinds (the thing the bus driver adjusts to show you the destination of the bus). You can sometimes still see these being used on buses, but I had never imagined what the full blind would actually look like.