I stayed at the hotel right beside the bridge on the City side, I think called the Thistle Tower Hotel, some time back. It was great as we went to things we hadn't seen before, dockyards, HMS Belfast, the Prospect of Whitby pub, as well as more City churches and so on, with actually quite a bit to do and of course the tube made it easy to go to the west end. However, it was about our sixth time in London that time, and if you have visited less often there are areas much more pleasant for walking and evening activities. We really like the West Kensington area south of Hyde Park and west of Harrods. Lots of places to stay at reasonable prices with easy access.