I feel the need to reassure you about East London! It's not the best side of town, but I lived there for 4 years, with young kids and no problems - never saw any violence (maybe I didn't go out enough??!!). Anyway, my point is that East London and surrounding area is very large and very diverse - it's not San Diego, but you should be able to find somewhere you can be happy!
You may want to look at the following areas to get an idea of how different various areas can be ... hey, and don't forget the Olympics may be coming to East London in 2012!
Canary Wharf/The Docklands - HUGE upscale waterside office/shopping/housing development, lots of money, very clean, good transport links, don't know much about whether there is a sense of community though?? Look at
www.canarywharf.comHackney - multi cultural, rough and ready, with pockets of gentrifcation, nice parks, Victorian housing
Walthamstow - a bit like Hackney but perhaps a bit less rough and ready??!!
Wanstead and Woodford - former rural villages, now on the tube and very much suburban - but nice atmosphere, lots of green space - good houses, shops and schools on and guess what, expensive!!
Chingford - a cheaper version of Woodford - I lived there and found it very pleasant - we had fantastic neighbours on our street - we still go back and visit them.
Good luck!