Nielsen Park in the Sydney Harbour National Park hosts a very popular family beach called Shark Beach. Located in the Vaucluse suburb in the east of of Sydney and facing the Shark Bay, this beach gets it name from the fact that it faces Shark Bay and is protected by Shark nets. To reach the beach the the bus no. 325 that will take you right along Vaucluse Road to the back of Nielsen Park from where it is a ten minute walk to the beach.
This tidal beach is a popular place for it has plenty of green shaded space, calm water with a hint of a swell and a shark proof net. It is only 400 metres in length, with shallow waters and also has tiers of steps lead up to an esplanade and behind that is an extensive park. Kiosk, toilets, picnic tables, barbecues, drinking water and proximity to the city make it one of the preferred places for family and corporate picnics. This beach and the adjoining Nielsen park is also a good vantage point for viewing the yachts in the Sydney Hobart Yacht Race.
Check out some pictures of the beach here and here. The adjoining Nielsen Park is a starting point for quite a few coastal walks including the famous Hermitage Foreshore Walk.
If your idea of a picnic area is a patch of grass or a flat rock to sit on then you will find multiple places to sit down in this area and enjoy the view.