The AA is Britain's oldest school of architecture, but anyone can take advangte of the great work going on there. You can catch really interesting public lectures and free exhibitions throughout the year. There are also occasional installations and event launches, a bijoux cafe and brilliant bookshop. A great place to hang out with the builders of the future.
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.