Most of that information is correct. The beach at Conwong or little conwong is very close to the bus stop for La Perouse, easiest way is take the L 94 to the last stop. It is still popular and a very good place to swim but by may will be a little cool, right now the water is great warm and clean.
You can take a ferry to watsons bay from Circular Quay and is one of the best trips in Sydney. lady Bay is a short 10 min walk towards south head, although a track passes by the top of the beach it doesn't create a problem. The beach faces north and is well sheltered from wind and is a natural amphitheatre, nice to swim at and great views down the harbour and across to Mosman and Manly.
Cobblers and Obelisk are at Middle head, a nice way to get there is by ferry to taronga Zoo then a 239?? bus up the hill to Balmoral, get off as the bus swings down off Middle head road and then a short 5/7 mim walk down the hill to the oval and on the north side is Cobblers , directly across from the oval or south past the car park to Belisk, a nice swimming beach but essentially gay. The swimming is good but the lower sun will encroach and creat shaows.
Cobblers faces north and has grass sections etc but the swimming is not as good, a different crowd as wel.