Best society/locale in central/south Mumbai for families with a decently large rental budget?

We have a pretty big (but not huge) rental budget and I'm wondering what societies/locales are best. Preferably in South Mumbai. Currently staying in Dadar West/Prabhadevi area and paying 1.6L for a tiny flat in a building with no amenities. We have small kids so are wanting to explore what better options might be out there.

The big thing is a place with play area(s), green spaces, ideally a pool, and so on.

Preference given to Dadar, Worli, Prabhadevi, Lower Parel, Parel, Matunga, etc. The area has to be safe to walk around and convenient. That is also very important.

What would your recommendations be?