Go to the South Bank and have a tour around the Globe Theatre :::
http://www.shakespearesglobe.com/
Or take a boat trip down the river to Greenwich. Fabulous trip down and plenty to see when you are there. Come back to central London by using the foot tunnel under the Thames ( ! ) and get the Docklands Light Railway.
If you want a meal out, by the river, try Hays Galleria ::
http://en.wikipedia.org/wiki/Hay%27s_Galleria
Or take a tour inside Tower Bridge ::
http://www.towerbridge.org.uk/
As you can see, I am a huge fan of the "other side" of the River !