I left Thursday night from New York with my 17-year old daughter and we stayed until Tuesday afternoon.
We stayed at the Thistle Marble Arch (see my review). The weather was in the 50's, overcast every day with slight drizzle.
It was my first trip to Europe for my daughter (I have been many times) so we did a lot of touristy stuff. On Saturday we did the Tower of London tour and it was great of course. The second half of the day we went to St. Paul's which is a wonderful piece of architecture.
Food is E-X-P-E-N-S-I-V-E. For example, a pizza at Pizza Hut will run you close to $20. I don't know how you can spend less than $100 for a decent dinner, or less than $50 for lunch.
On Sunday we did Madame Tussaud's which was more fun than I expected. We had a great time and I would suggest that you get there early. That night we did the "Jack the Ripper" walk. It lasted about 1 3/4 hours and was quite fun.
Monday was Westminster Abbey. Make sure you take the guided tour since you get to go to parts of the Abbey that are not open to the general public. That night we went to the West End to see "The Producers" which was fabulous. I would recommend that you go during the week when it is less crowded and probably less expensive than the weekend.