I agree with @liuzhou that it's a good idea to head over to Borough Market (which is only a 15-min walk away), given that there isn't much interesting around Tower Bridge. Last time I was in the area, I had a nice lunch at Wright Brothers (disclaimer, it's been a few years). The whiskey exchange is not to be missed if you are looking for a "souvenir".
I would recommend checking the guides from Eater, they generally have good recommendations, including some by neighborhood including one for Borough market that is fairly recent. They also have this nice guide here.
If I were you I'd hop on the tube and go to St John...
