This part of the city is pretty suburban. If you spend more than a few days in Sydney you will probably head over the bridge to check out the northern side of the harbour here. If you go a little further there are some interesting things to see and do. There are some great spots to view Sydney's fireworks here.
Some nice walks through here. You have to pay to park in the National Park but there is lots of parking outside. In particular Plassey Rd. There is a large cave near the park entrance on Carramar Rd. Walk in from Carramar Rd and when you hit the main track turn right. The cave is a short walk from here and if you go past the cave there is a nice waterhole.
Lots of great walking tracks here especially Resolute Bay, America Bay & Great Mackerel Beach. The main campsite is called The Basin and is very popular. Pays to book ahead for this one. The best way to get to The Basin is via the ferry from Palm Beach Wharf on Barrenjoey Rd. Tickets are $16.40 return. Great campsite with a party atmosphere in the summer $34 for a site.