Wow! I read your post and thought, "this was me 3/4 years ago".
We lived in a gorgeous area, 40 miles out of London, right by the Thames in a small town that had become very hip and happening, hence lovely shops and restaurants had moved in, the schools were fab, 2 min walk to feed the ducks by the river, play in the park etc etc.
I was very settled, then dh said he had to move back to London. He needed to for his career, but I was royally pissed off.
Anyway, we moved and 3.5 years on I'm happy here.
We live in Ealing in an area called Pitshanger Village. It really is like a village, but we are still in London. if you can move into the catchment for North Ealing Primary School, even better, or there is St.Gregory's if you are Catholic.
Fab pre school playgroups close by, plus the Ealing 135 Group for parents of young children - bit like the NCT, but better IMO. Pitshanger Park has a playgroup for small children every week day in the summer, with both indoor and outdoor activities.
Pitshanger Lane is a traditional little shopping area - small library, chemist, organic butcher, supermarket, fruit&veg shop, bakers, hairdressers, beauty therapy centre, childrens shoe and toy shop, delicatessen, coffee shops, cafe's etc etc.
There are loads of clubs and activities for children, either run in the 2 church halls, The Brentham Club or at the dance centre on Pitshanger Lane.
Some of the houses around Pitshanger Lane form part of The Brentham Estate, which is a Conservation Area, and very pretty.
For £670k, you should be able to get a 4 bedroom property.
The only 5 bedroom one I took any notice of recently when it was up for sale (because it was my favourite house in the area) was on the market for £900,000, but it's a special and unusual house, so there may be 5 bedroom properties round here in your price range.
I just thought I'd give you a run down, because I've been surprised by how pleasant it is round here, despite my initial deep reservations.