The Clifton Gardens Pleasure Grounds (fancy shmancy) surround the lovely Chowder Bay in Mosman, and is a great place for an afternoon of picnicing, strolling, swimming, snorkeling, bird watching, and even a spot of fishing if the mood takes you.
There is a wharf, enclosed baths, change rooms, a modern playground, lots of grass, seating, several places to buy food (including Ripples Cafe), and some charming bushland to have a wander in.
If you have snorkeling gear then definitely bring it along, as the netting which keeps the chompy sharkies out plays host to a wonderful array of fish and even sea horses as can be seen from this array of critters.
The view at night with the lights across the water is quite spectacular, and night snorkelling/diving also provides the most rewards. The fishing off the wharf is obviously also better at night.
If you have the stamina I'd recommend a late afternoon stroll, then a swim, followed by a picnic to see the sun away and enjoy the lights, then some night diving (make sure you know what you are doing etc) or some fishing.
Remember if you do go fishing you'll need a licence ($6) which can be purchased online.
You should be able to find street parking without having to walk too far, or catch a bus to Morella Road. As always consult the 131500 website for your best public transport options.
Why? So much to do you'll need to go more than once.