It's been several years since I was in London, but my "don't miss" advice is the British Museum. I also enjoyed the hop-on/off bus and seeing The Phantom of the Opera at Her Majesty's Theater. And of course, I had a pint at a pub.
I was visiting a friend so wandered about on my own. I'm sure that I'd consulted guide books and Rick Steeves is a good one. He usually includes good maps. There will probably be instructions on how to get theater tickets, etc.
I stayed in Bloomsbury, near Russell Square and the University of London, a nice area for walking and convenient for restaurants and grocery stores. I remember picking up lunch at a grocery and eating in a nearby park.