if you are central - trafalgar, waldorf, green park - you are walking distance from lots of everything and tubes if you are feeling lazy
remmebr the tube map isn't 'to scale' so look on google maps.
the west end (soho/covent garden etc.) is small - it will never take more than 30 mins to walk anywhere.
tower of london is kinda more remote, its on the edge of the city (which is all offices really) theres lots nice round there - the tower, towerbridge, walks along the south bank (one of our favourite things to do is the walk from tower bridge to hungerford bridge (aka where the london eye is) along the river - you'll see loads. the tate, the globe theater, golden hind, clink prison, oxo building, southbank centre etc etc etc.
basically london is bloody brilliant
well i would say that wouldn't I