Where is the best place to stay in London?

I really want to go to London and see all the sights. However, I think that most likely it is only going to happen at the last minute when I get a deal on the airfare. That will leave me trying to find last minute London hotel rooms. Although I will have to book last minute, I would love to stay somewhere nice. Where is the best place to stay while in London? I want to stay in a nice area, even if I can’t afford to stay in a very expensive hotel. Can anyone tell me where I can get good deals on last minute hotel rooms?