Lots of buses and underground options give you quick access to Central London but we walked to Tower Bridge and the castle pretty easily ( in our early 60's). Be sure to see Churchill war rooms. One of the best exhibits on the war we have ever seen. Gives a sense of the fear also commitment of every person in London during those awful days. Shows a wonderfully complete picture of churchill and the working conditions of this amazingly preserved underground facility that was one of the first war command centers every conceived. Leave plenty of time for it all - three hours will allow you to hear the recorded memories of those who lived through it all and see the whole complex. This and St. Paul's leave you with a feeling of London at war.