Sydney's dog friendly culture means there are a great number of dog friendly off-leash parks around the place. Some of sydney's off leash parks are far better than others though so here's my pick of the best one for both owner and pooch.
Rushcutters bay dog park: The main area of Rushcutters bay park is off-leash from 3.30pm to 8.30am on weekdays and dog friendly until 10.30 on weekends and the darling point side of the park is off-leash all day everyday. The main area is where you want to be, with beautiful views across the harbour, looking down across the marina, a cafe at the tennis courts (or one in the marina who are happy to have your pup sit under you on a leash where you can pretend like you own a boat and be fancy) and the stairs into the water at the Elizabeth bay end make it simple for your dog to jump in, have a frolic in the water and cool down. The harbour steps are off-leash from 4.30pm-8.30am. There are always plenty of puppies to play with during off-leash hours and the dog owners are friendly.
North harbour park (at the bottom of condamine st on the balgowlah side) is another great dog park with water access. Dogs can run around freely and play on the beach. There's a small bike track for little ones in the park and a playground for kids to play in too. There's great bushwalks around to forty baskets beach too, you're technically meant to put the dog on a lead in those areas but locals rarely do.
The very far end of Clontarf beach is another great dog beach while you're on that side of the spit bridge. When you drive down there, don't go into the picnic areas but follow the road right around to the end (past the boatshed/marina) until you see puppies playing in the water. The beach is extremely flat so best to go at mid tide when there's lots of beach for the dog to run around and the water is just deep enough for the puppies to get wet, have a play and enjoy.
The dog beach at Rose bay is the final pick of the lot on my list due to its close proximity to shops, the size of the beach and the stunning views (not that the puppy will care) looking back across the city with the harbour bridge in the distance. To get there turn left of New South Head Rd just before the hill up to Vaucluse (just after the row of shops). There's normally a fair bit of parking available near the Rose Bay dog beach so it's a great place to take the dog for a swim if you have a car.
The first youtube video in the links was shot at Clontarf dog beach at mid-tide for reference and the second video is at the Rose bay dog beach (they get to the good part of the dog beach about half way through). Video 3 is of the dog swimming area at Rushcutters bay park off the stairs.
Be a good owner and take poo bags with you to the dog beach and leave the bags from your doggy beach excursion in a bin not on the sand!