Put on your walking shoes and follow the south bank of the Thames from Tower Bridge to Westminster Bridge. It's an almost traffic free walk and you will pass tons of interesting things/people, including ...
Butlers Wharf - super warehouse conversion into flats/shops/cafes
Tower Bridge - need I say more?
New City Hall - groovy new architecture
HMS Belfast - one for the military minded??
Something or the other Wharf (can't remember its name) - a filled in dock, lined with shops and cafes (undercover and warm!)
Southwark Cathedral - ancient and atmospheric
Borough Market - on a Saturday - foodie heaven - tremondous - stop here for lunch
Replica of the Golden Hind ship - one for the kids??
Wine museum - very interesting
Old pub - can't remember its name, but it's old and good
The Globe - Shakespeare's theatre - aboslutley brilliant
The Tate Modern - zowee - big power station now art gallery
Gabriels Wharf/Oxo Tower - arts/food complex
South Bank Arts Centre - incl Museum of the Moving Image, National Theatre, second hand book sale udner Waterloo Bridge
... and great views of London all the way along, lots of places to stop/visit/eat/drink/recuperate.
I know that's not one place, but it's a god taster!