Personally, I would look for areas on the tube/DLR rather than the train services into London Bridge (I really didn't enjoy commuting by train from southeast london, just my two cents). There are indeed some really nice areas not far from Tower Bridge along the river, like Limehouse. I also think Canary Wharf/Docklands might be too sterile, coming from Chicago.
Don't forget the south side of the river! There are some really nice parts of Borough/Southwark that you may be able to afford and your husband could probably walk to work, and you could walk nearly anywhere. This is one of the oldest parts of the city and might be more appealing than some of the rejuvenated areas east of Tower Hill.
Bottom line, it's hard to recommend areas of London because the city is so huge and each neighbourhood varies so much even within itself... and as you see, people have very strong opinions about where they live! I really recommend checking out places for yourself and not relying on reputations, if you can -- I always hear my neighbourhood is super dodgy (it's really not) and I've been surprised to see that areas I always heard were really nice didn't seem that great to me, or seemed kind of boring (I'm from NY/DC).
If you can get a temporary flat for like two or three months while you're looking for something more permanent, that would probably be ideal, so you can see things for yourselves...