London is so vast I end up spending hours travelling on trains. They are by far the best way to travel around on and are always full of weird and wonderful characters.
The Greenwich Observatory with its green laser beam can transfigure any night sky. If you decide to cross the Thames via the foot tunnel, make sure you look out for the green ray. You can be on one side of the meridian in a minute, and cross to the other side on the next, without even realising it.