I couldn’t say about playgroups and the like. But I’d be a bit surprised if there was much of a young parents’ community in HGS. I’m happy to be told otherwise though.
The pupils at Henrietta Barnett school (which is super selective) come from miles away: it’s not really a local school in that sense. There are one or two state primaries in the area I believe (Brooklands?)
There used to be classical concerts in the square every summer but apart from that I’ve never heard of HGS community events. Again, though, I don’t live in HGS and someone could well say differently.
There is some greenery around HGS, including the Heath, so park outings could certainly be done.
My main objection to living in HGS though is that you’d have to travel for absolutely everything. There is not a single grocers, hairdressers, newsagent, cafe, coffee shop, restaurant, pub, bank, post office etc etc in the entire place.
Depending on where in the ‘burb you live, Golders Green could be a decent drive away.