Just finalizing some plans today. I will be there for a week in October, staying with a friend. Excluding Niagra Falls, I have never been out of the USA.
Any advice on what to see/where to go is appreciated.
Try to take in a show at The Globe. I went to two while in London, and they were both magical. But book your tickets well in advance unless you want to end up waiting in line for nearly two hours for a shot at cancelled seats like I did the second time around.
I thought Westminster Abbey was really cool. I am fascinated by British History and it was very exciting to see the tombs of Elizabeth I, Edward the Confessor, Henry V and many other monarchs (plus tons of lesser nobles). In the South Transept are buried Chaucer, Alfred Lord Tennyson, Dickens, Kipling, Handel, and Lawrence Olivier, among others. The Chaper House is from the 13th century (can you imagine anything that old?) and still has some of the original floor tiles!! There is a lovely garden out through the back as well. Plus, where else can you say, “Oh ho! I’ve just stepped on Charles Darwin!”
Okay, I’m really boring.
Depends on your personal interests. I second the Globe, but then I know some people who would never take in a Shakespeare play. With a week, you could even be daring and take the Eurostar to Paris for a real “out of USA” feel. Spend the night, walk around the Latin Quarter, hike up the Eiffel Tower and the Arc de Triomphe, eat delicious French pastries in the presence of dogs (pets). Ooops! I guess the focus here is London. Well, I found the Millennium Wheel (London Eye) fun for photos and views, and the London Dungeon was interesting (something to do once). Your friend might know about the Ceremony of the Keys at the Tower of London (see The Ceremony of the Keys – Tower of London Tour). You have enough time to get reservations or tickets in advance for some things. You’re going to have a wonderful time whatever you do! 
When you get off at the airport there are usually lost of pamphlets advertising all kinds of things ** take the one that has the walking tours **. My Wife and I did several of these and they were great. They range in price from 5-10 pounds. Basically you show up at the entrance of a tube station at an appointed time and away you go. ** HINT ** : take the Jack the Ripper walk. The nice thing about the walking tours is that they often take you to places that the big tour busses don’t go.
We also did the one day pass on The Big Bus Company ( I think that’s what they are called). Basically you buy a ticket and you can hop on and off the bus at certain stops along the route. They do take you to all of the high points in London
If you are thinking of taking in a show the best price for tickets are at Liecester Sq. There is a booth there that will sell returns / unsold tickets for that days performances often at a discount of 40 - 50% of the listed price. We also found www.londontown.com REALLY helpful.
Take in the Museums & Galleries. They are often free (or request a donation). If I remeber correctly the National Gallery and the British Museum were set up like this. Just think you can see Vincent’s Sunflowers, Monet’s Water lillies and the Rosetta Stonefor minimal cost. London is an expensive city so take advantage where you can.