Here's a great two mile walk. You could easily spend 2-3 hours and see many of the major sights.

For example: start in Piccadilly Circus (sort of a mini Times Square), walk over to Leicester Square (always movie premieres going on and other activities; TKTS booth), then to Trafalgar Square (National Gallery art museum), then down Whitehall Street toward Parliament (passing by Prime Minister's 10 Downing Street). Parliament Square is right there then cross the River Thames (great photo op looking up to Big Ben).

Once you cross the Thames you can some other great sites going down the South Bank of the river (still only walking): the London Eye, Film Museum, National Theatre, then if you keep going to the Tate art gallery and the Globe Theatre (Shakespeare) and eventually the cool Millennium Bridge over to St Paul's CathedraL.

You can decide what stuff to go in and see. But that's a great little 2 mile walking tour.