Do you like walking?
Here is a circular walk you could do along the River Thames (it is actually a run but you could walk it). You would be starting from the right hand end.
It is 7 miles but you could easily skip a bit by crossing on another bridge or using the tube or bus to take you back ot the hotel.
http://www.serpentine.org.uk/routes/04/
This walk would take you to all sorts of interesting places including:
Tower of London, Tower bridge, the Tate modern art gallery, the famous "wobbly bridge", Shakespeare's globe theatre, the London Eye, Houses of Parliamant, plus various famous boats moored on the thames.
On a sunny Sunday this would be a wonderful stroll.