It's a bit difficult to say how much your travel costs to London might be, because we don't know where you're starting from!
An off-peak Travelcard (giving you unlimited travel on Tubes and buses after 0930 on weekdays or any time at weekends) will cost you £5.60.
The major national museums and art galleries are all free (except for optional admission to certain special exhibitions). They include the Science Museum, the Natural History Museum, the Victoria & Albert Museum, the National Gallery, the National Portrait Gallery and Tate Modern (as well as loads more).
Theatre tickets can be very pricey (and, for the really popular shows, booked out many months in advance). Expect to pay £40 to £60 per ticket for many shows. However you can usually find something that you'll like if you buy on the day at 'tkts' in Leicester Square:
http://www.officiallo...kts/leicester_square/
The best value food in central London is at the excellent 'Bistro 1' chain, where a 3-course lunch costs £8.89 (that's £7.90 + 12½% service charge):
http://www.bistro1.co.uk/bistro1/Home.html
Chris