We just got back from London. Were there for 9 nights. Stayed in an apartment instead of a hotel or B&B and wouldn't do it any differently again. We could eat breakfast at our leisure and wearing our PJ's. We were able to also stop at the grocery store and buy fresh fruit and eggs and bacon and cook our own breakfasts. It was super comfortable!
The London Bus was our number one favorite mode of transportation. Using an Oyster Card really made it easy, we bought the one week travel pass and then afterwards we just put 10 pounds in to each card to last the next couple days.
London has so much to offer, 9 nights is just enough to skim the surface yet also get a good feel of the city.
Rick Steve's map is a priceless resource for finding the sights and interesting streets. I also had a Phillips London Guide which is better than the London A-Z so popularly sold there (found the Phillips version at Half Price Books here in Seattle for six bucks).
If I were traveling alone I would stay at a budget hotel like easyHotel but my wife and I appreciated the comfort of an apartment, a real home away from home! english-manner.com is the website we rented through. Glo in Los Angeles is a real super person to deal with.