A Day in London

[ChromePony]

So I'm flying into Heathrow this Sunday at 7AM and I have a flight out of Stansted at 5PM. This leaves me more than enough time to spend a nice quick day in the city. I'm looking for ideas on how I might entertain myself, keeping the time restrictions in mind. I've been to London before, saw the Tower, Big Ben the Bridge all that good stuff, as well as the Tate Modern and some of the main touristy areas. Since I'll probably be a little jetlagged, I'm thinking it might be nice to catch another museum or maybe just stroll around some nice but less touristy neighborhoods. I'd also like to keep things cheap and avoid even taking cash out if at all possible since the pound kicks our ass so hard.

I've already done some research and I know there are plenty of resources out there, but seeing as how so many londoners hang out around here I thought it would be nice to get some inside input. I can come up with plenty of things to do, but the hard part is deciding whats reasonable in such a short period. Also, geography and transportation is kinda key cause I dont want to waste my whole time sitting on the tube. Thoughts?