London is indeed a fascinating city. Wherever one walks there is history. There is something for everyone.
North of Trafalgar Square is the National Portrait Gallery - and free (charge for special exhibitions). I particularly liked the 500-year old portrait of Elizabeth I. My favorite was the British Museum - in my opinion the greatest collection of antiquities assembled under one roof in the world and free (charge for special exhibitions). The Bank of England museum was quite interesting - and free.
Hampton Court was an experience - the haunted gallery, the chapel, the royal apartments. I could imagine Henry VIII and his entourage arriving by royal barges from Whitehall Palace. Enjoy!