I've only been there once, and very briefly, but here are a few suggestions:
1) dress WARM! you'll be there in Oct. it's bound to be cold, wet and windy.
2) you HAVE to take a double decker bus tour - you'll see everything!
3) the Tower of London is a fascinating tour, so I hear anyway.
4) visit a local pub for lunch or dinner, nothing like an authentic British
5) look for a live theatre play. (like a Broadway show) I don't know what's
playing in London right now, but I'm sure you could look it up. I saw a
great one called Starlight Express!
6) I also heard you can take a "Harry Potter" tour, of the studios where
the movies are filmed, and the castles as well.
That's all I can think of for now, have fun!