right, bit slow to return, and it seems most of what I was going to suggest has been mentioned above.
I would add...
Avenue house and victoria parks both have cafes and playgrounds. There is also the dollis valley green walk, which actually goes on for miles, but has some fab scooting terrain as it passes through west finchley.
Long Lane Pasture. Go down long lane, cross squires lane, past the fire station on your left (look out, they do open days which are great fun), just before the bridge that carries the north circular, turn right and follow the pathway up a slope. follow the fence and there is an entrance gate. it's open 9-5 at weekends only, and is a sort of nature reserve, with bees, butterflies, meadow, wild flowers. It's actually a proper hidden gem.
Sadly you can no longer play with the animals at college farm on regents park rd, between gravel hill and henley's corner (you could when I was a kid, but it's been closed for about 20 years I think). But they often have the horses out in the paddocks, and you can lean over the fence and pat them.
The secret entrance to avenue house is located on The Avenue. It's a narrow road off Regents park rd, opposite the Two Brothers fish restaurant. It doesn't look too promising but head down the little hill and you are there. If you follow The Avenue all the way to the top you get to squires lane. this would be a good short cut to long lane pasture (turn left onto manor view, then right at the lights onto long lane).
Golders Hill park, which is golders green really, but has a collection of animals, a nice if pricey cafe, a newly re-vamped adventure playground, and a playground with sand pit for littlies.
Belmont farm: petting farm. Costs money but quite good fun. I think you can get the 221 bus there from golders green.
The cafe at the bottom of east end rd is called Barista I think. They had a legal isshoo after someone tripped on a buggy, so you have to leave the buggy outside. Not great if you have a buggy!
Creativity crazy opposite the lido, on the high rd at the end of squires lane is one of those pottery painting cafes. the pottery painting is £££, but it's a nice way of making a memorable gift for a grandparent, and they also do messy play activities.
if you don't mind heading east, there's a nice music group called Al's little singers at the clissold arms pub on fortis green. i think its monday, wednesday and friday.
Stay and play at fairway children's centre and at mill hill library are both really fun and good value, though a bit awkward to get to unless you drive.
this website sometimes has useful stuff.
this website has lots of stuff if you are interested in jewish groups.