Thank you for all the advice on where to stay in London. I think I have picked the County Hall area. Next question....do I purchase a London Pass book?
Nope. All major museums are free. As well as the Tower of London, you will pay as a tourist to enter Westminster Abbey and St Pauls Cathedral, but you can get around that even, if you are content to see both as a worshipper attending a service. The Tube can get expensive but County Hall is close to many sights, so walking will be a good option in many cases for you.
Remember that while the pass will say that it covers (for instance) 80 attractions, you can only see 2 or 3 in a day. So it's very hard to make a pass pay off, particularly on a short visit. That said, there were some recent threads about people who bought the pass and were happy they did. It all depends on how many covered sights you are seeing.
I there's more than one of you going, the Two for One deals from Days Out can be a very good deal. Some details here: http://www.tripadvisor.com/Travel-g186338-c195600/London:United-Kingdom:2.4.1.Travelcards.Step.By.Step.html
The London Pass can be a good idea. you have to do the math and be realistic about how many sites you will see. If you are going to the free museums, no, you do not need it. But Westminster, the Tower of London, many of the palaces, London Zoo, London Eye, etc., are covered. Note that London Walks gives a GBP 2.00 discount for each walk you take if you have the LP. Do your itinerary and a spreadsheet.
Really liked the Oyster Card and highly recommend it. We ordered them in advance so hit the ground with them, no need to stop and buy them in London. Just topped them up once when we ran low.
If you are spending all your time in London you can visit a lot of free Museums and Monuments. Some of the historic homes and specialty museums in Greater London belong to the National Trust UK. Check out their site to see if you would like to visit properties on their list. They have an Overseas Visitor Pass for different lengths of time. If you haven't seen the big Museums...see them first.