I'm not sure what your budget is but you should be able to get a decent room in London for 150 pounds a night or less, it should help offset the travel costs and time in and out of London. Try some of the smaller family run hotels rather than the big chains, they are much more friendly.
I would:
- Buy and Oyster card, you can top it up when needed and works on all regular tubes and busses and is quicker & much cheaper than buying travelcards daily.
- Walk through Hyde Park & regents Park
- See London Zoon
- Take Half a day around the Tower of London
- Catch a boat down to Greenwich (You can get a tour pass) & see the Royal Observatory
- Walk along the South Bank of the Thames during the day and especially in the evening (V. Romantic)
- See Stomp or another West End show, last minute tickets are available from a stone booth in Leicester Square
- Only shop in Oxford Street & Regent Street if you are an absolute shopaholic, they are pricey, busy and difficult to find stuff.
- Go on the London Eye, again during the day, or the evening if you can.
- Take good shoes, theres a lot to walk and see, or catch an open top tour bus.