Tower of London. (Hint- it's a castle.... don't be an Ugly American like we were...
) Walking distance from Picadilly Circus. A block off Picadilly Circus is the Queen's Theater. We thoroughly enjoyed Phantom of the Opera when we were there a few years back at Christmas time. I'm not exactly an opera type, either... but I'm betting whatever the production - it's worth it.
Just don't ask anyone for directions in P.C.. It took us 7 tries to find someone who spoke English. Look for someone dressed in vest and suit...
Not kidding! Britain is doomed!