Originally Posted by
Swiss Tony
You can then get off, visit the Tower of London, then - if you're up for it - start walking towards Monument. There's a tower here that was built after the Great Fire of London. From there, walk North up Gracechurch Street to Leadenhall Market , then down Cornhill to The Bank of England and Royal Exchange. From here, keep walking along Cheapside and you get to St Paul's Cathedral.
One detour worth doing at this point might be to go up to the Museum of London which is a good insight into the history of the place.
As an alternative to this (which is a bit architecture focussed so that may/may not be the OP's "thing"), after finishing at the Tower of London, I'd have a "refreshment stop" at St Katherine's Dock then walk across Tower Bridge and continue along the south bank of the Thames heading West. Passing City Hall, Hay's Galleria, London Bridge, Borough Market, Thameside, Shakespeare's Globe and on reaching Tate Modern, crossing the Millenium Bridge (footbridge) to St Paul's Cathedral. If the OP is still full of energy, I'd then cross back and have a look around Tate Modern (it's free!) and carry on as far as the South Bank, then back over the river to Embankment. On a bank holiday Sun/Mon, this whole walk will be busy with lots of street entertainers/stalls etc and give a really good feel for both old and new London whilst ticking off some of the OP's required tourist sites. Plenty of cafes/restaurants/pubs to stop off at on the way.