The Unfinished City is home to hundreds of museums, the majority of which are free to enter. Currently my favourite museum is the Museum of London, which charts the history of our great city from prehistoric times right through to the present day. It is an absolute joy to explore and I always learn something new, from each visit.
Having said that, until recently I had never explored the entire museum. This was usually because of time constraints, or popping in for a quick exploratory, while waiting for the rain to alleviate.