This posting is part of the 30 day challenge...
I could have chosen many wonderful places I have visited, but have decided to keep it simple... and a little more local for those who may be visiting London and have half a day to spare.
My recommendation is the Thames Path from Tower Hill tube to Greenwich via Rotherhithe. This 6 mile route takes in some of London's many historic sites and apart from a dodgy part in Deptford, it's a very pleasant journey that is mainly along the Thames.
You can cycle or walk the whole route and there are plenty of pubs and restaurants to stop at. You get to see Roman ruins, posh yatchs, Tower Bridge, modern buildings, ancient buildings, parts of the old docks, wildlife (yes, in London!), the best view of Canary Wharf, some lovely old pubs and Greenwich, which is a great place to visit anyway.
My preferred walk is shown below, but there are two options for the first mile or so. You either cross Tower Bridge or walk via Wapping and then the very very short train ride under the Thames to Rotherhithe.
Tower Hill Underground
Lookout and Roman Wall
The Tower Of London
St Katherines Dock
Tower Bridge crossing the Thames
The Angel Inn
Stave Hill and Ecological Park
Hilton hotel (for the views)
Greenwich town centre and market
Greenwich Park and Observatory
If you still have some energy, walk through the Greenwich foot tunnel, through the Isle of Dogs and up to Canary wharf.
I am happy to provide more information if you leave an email address on a comment.