(2-part post)
Hello again.
The area around Tower Bridge doesn't have that many attractions which leap into my mind, but that hardly matters because the whole of central London is within a few minutes ride on the Tube.
In the immediate area, the main tourist attraction is obviously the Tower of London:
http://www.hrp.org.uk/toweroflondon/
It's quite pricey and it wouldn't feature in my own list of the best places to go in London, but it might appeal to you.
For me, HMS Belfast (which is anchored, on the south side of the Thames, close to Tower Bridge) is far more interesting:
http://hmsbelfast.iwm.org.uk/
OK, I'm a fella' and such things are often viewed as being principally of interest to 'big boys' but I think that you'd enjoy it. (Wear 'sensible shoes' and be prepared to climb up and down a few short ladders).
If you're looking for some classy bars and restaurants in that area, try St Katharine's Docks. (On the northern side of the Thames, immediately east of Tower Bridge).
Alternatively, there are some less expensive places to eat at Hay's Galleria:
http://www.haysgalleria.co.uk/
(On the South Bank, just past where HMS Belfast is).
Heading further west, Tate Modern is on the South Bank:
http://www.tate.org.uk/modern/
(Admission is free so, even if you're not really into modern art, it's worth a look).