Okeydokey here's some ideas...(assuming nice weather..lol)
Day 1
(optional if you're an early riser) - Hop on Northern line to Hampstead, have a wander on Hampstead Heath and get a glorious view of the whole City, brilliant. Wander back to the Tube and grab brekkie in a café then hop back on the Northern line and go to:
Chalk Farm. Come out of the Tube and walk down into Camden Town, visit the market/High Street then go down onto the canal and walk to the Zoo and have a look around which takes you to lunch - pop back into Camden or go to Primrose Hill and get something there.
After lunch, walk down through Regents Park (you could even go by Madame Tussauds if you want

)and then on to Oxford Circus. Wander along Oxford St (OMGZ shopz

) then cut down through Soho to Piccadilly Circus and then to Leicester Square, then round to Covent Garden just in time to grab the pre-booked pre-show meal & show deal (lastminute.com) and watch a show in the evening, have a few drinks afterwards then head home.
Day 2
Hop on the Overground at New Barnet to Kings Cross then Circle Line to Tower Hill. Check out the Tower of London, Tower Bridge etc. Walk through the City along Bishopgate and see the Lloyds building, the Gherkin, Tower 42 etc, walk to Bank and see the Royal Exchange then:
alt 1. From Bank you can walk to St. Pauls Cathedral, then cross over the Millennium Bridge and check out the Tate Modern, have lunch around there.
alt 2. Walk to and cross over London Bridge and go to Borough market and get lunch there. Walk up to the Tate Modern and have a quick browse. Cross over Millennium Bridge, see St Pauls, walk along North Bank and cross back over Blackfriars bridge.
Then walk along the South Bank, check out Globe Theatre, London Dungeon, Millenium Eye etc, wander along all the way to Westminster. Cross over the river there and see the Houses of Parliament, then walk up through Whitehall and check out Downing St etc and you find yourself in Trafalgar Square. Walk up to Piccadilly Circus then go into Chinatown and get some awesome Chinese food, then afterwards go to 'Ain't nothin but the Blues', a cool venue where they have live music etc on all the time and have a few beers then head home.
Day 3
Overland to Kings Cross, Victoria line to Oxford Circus, then Bakerloo to Lambeth North/Elephant & Castle. Walk to Imperial War Museum and check it out. Afterwards, hop on tube to Embankment, then get the Circle/District line west to South Kensington. Eye up all the posh totty, then go to the National History Museum/Science Museum/V&A (any/all 3 + lunch somewhere in between). After museum, walk up to Hyde Park then wander along to Buckingham Palace, then walk along Piccadilly to Green Park and then back into West End.
*phew*
