Hi
I can only really comment on Tower Hamlets as we live in Bow. To be honest, I think that if you are looking for a family house, you may have missed the boat with the house price rises. You don't get much change from half a million for a three bed terrace around the conservation areas/Victoria Park (we are currently selling our flat in a mansion block and moving to the country).
Period properties are at a premium, which most family places are, if they are not maisonettes on estates. The post-olympic development of the site itself looks pretty impressive, but there are a lot of homes being built on the site, which may mean that there are enough to meet demand.
So, I think that it would be an okay place to move to, but it is expensive and I am not sure prices will soar in the way people have been saying. Also, we have found it really hard having a baby here (in fact, I've decamped to a cottage in Norfolk 'til we move (!)- it has been hard to access health services for my daughter as there is such a high level of need, there is crime and pollution. I am not sure that you'd move to east London for the quality of the schools- everyone I know has either moved out by school age or gone private, which is hard as there's such heavy demands for private schools in the area. Of my six antenatal class pals, there's only one left in TH a year later...
Don't want to sound really down on Bow or east London, as I've been really happy there, but I'm just not sure it's a great choice if you are looking for a bargain or great schools.