Moving to London. Seeking advice on Neighborhoods

[Britv82]

Hello Mums! Would any of you kindly share your thoughts on great places to live with kids (girls) ages 7 and 9? My family is relocating to London from the US in June for my husband's job. He does not have an office to report to (he is in sales with the whole of London and the southeastern UK as a territory so we can live anywhere really) which makes it a bit harder to decide on location. He will have to travel out of London a good bit so getting out the city fairly easily is appealing (we will have a car). We have explored SW London a little bit and liked Wimbledon, Teddington, Chiswick, Wandsworth/Clapham. Any thoughts on Barnes, Southfields or East Dulwich? These keep coming up but we have not visited in person yet.
Here is what we are seeking....can you help identify a nice place for a family or give your thoughts on the above places if you live there?

1. Good state primary schools (feel free to name a great school to visit or send me a private message with recommendations! My husband is moving over in April so he can do a visit)
2. Good secondary school as that is coming up in 2 years
3. Strong community/family feel (we consider ourselves very social) :)
4. Good transport links
5. Green spaces & access to sports/fitness options
6. Good variety of restaurants and cultural activities
7. Our top end budget is about 4000 a month (renting - not buying)

I know this is a bit of a broad question and likely everyone is seeking this :) but we are overwhelmed and would so appreciate any bits of guidance from fellow mums! Thank you so much!

Yep, that’s why I listed the primary feeder schools. OP doesn’t have secondary kids yet so as long as she can get into one of the primaries mentioned, she should be ok for Bolingbroke.

I live in a lovely part of SE London. Waterloo is easily accessed via the overground and then jubilee line. Getting out of London - particularly over to the M4 can take ages. It’s taken me 2 hours on occasion.

East Dulwich is nice although transport links aren’t as good as Peckham (although easy to get to). I also really like Herne Hill.

I’d recommend where I am except I’m not so sure secondary schools are that great.

How about north london eg East Finchley /Muswell Hill / Highgate / Alexandra Palace? I believe all have great state primaries & secondaries. Plus, if you decide to go private later on there are lots of options nearby.

Nice green spaces, quick public transport into central London, easy road access to travel out.