Thanks for the replies...
Don't worry about the money, we are fully prepared for that (and $80 is kinda normal for us)
Has anyone ever heard of a hotel called The Connaught? It's in Mayfair, reasonable by what we are looking at, and expedia rates it 5 stars (I am aware the standards are different there).
The Red Bus tour sounds kinda fun for a first timer, we'll probably try that, and the Tix booth sounds like the way to go for the show!