As I've mentioned earlier, the Bombay I grew up in was a much more laid-back city than it is now. It was also a much smaller city. In those days the Aarey Milk Colony(was what it was called) was far out of the city and we were taken there as Junior School kids, as a one day excursion out of the city!
There were more open spaces in those days. We were taken to the Malabar Hill gardens quite frequently, where there was a boot shaped slide--more like the 'Old woman who lived in a shoe' kind of thing--a boot with a roof on top. I wonder whether it is still there. Once we moved to Bandra, the Bandstand was a favourite spot for a quick visit.

Juhu beach was not the hip and happening place it is now and we went often to swim there and I think there was a club nearby which someone in the family was a member of.

There were lots of eateries we were taken to as both my parents were adventurous in their food tastes. I remember the Irani restaurants for the falooda and pattice; then there was Nanking's Chinese restaurant (the one near the Royal Yacht Club) near the Gateway of India, a regular haunt; there was Bombelli's bakery at Breach Candy (not there any more) which had the most moist chocolate pastries. Then there was the Parsi Dairy farm icecreams, hot jalebis--somewhere Worli side is what I remember faintly--bhelpuri around the Breach Candy area, absolutely delicious Kala jamuns and rosogollas which were brought to the house in big clay pots (absolutely unthinkable now I'm sure), gingerale and some other fizzy soft drink, all inextricably linked to my memories of Bombay.
Of course now Bombay has more than enough famous eateries and the bhelpuri and hot jalebis are available in so many places. But I promise you that those absolutely black and sweet gulab/kala jamuns were to die for and I've never had stuff like that afterwards.