There are a number of suburbs which make up a part of the city and also surrounding the city. Darlinghurst, Kings Cross and Paddington are inner-city suburbs situated to the East of the city. Moving further east you'll come across the upper-class suburbs of Double Bay and Vaucluse.
If you are looking for a beach resort visit Bondi or Coogee, South East of the city. West of the city is Pyrmont, Newtown and Leichhardt, along with Glebe and Balmain, two peninsula suburbs. The Western suburbs end at the Blue Mountains 50km from the city, including the Parramatta and Penrith settlements.
There are 4 airports in Sydney, although the main airport is the Kingsford-Smith Airport. The Kingsford-Smith Airport is in Mascot on Botany Bay, which can be found South east of the city centre.
The suburbs in the North part of the city are called the North Shore. They stretch 20km North of the city centre. The suburbs also stretch 20km South marked, like the North, by various National Parks.
There are also plenty of areas close enough to Sydney to be suitable for a rewarding day trip or longer stay. Heading about 1 hour west you will come across the marvelous Blue Mountains, which offers spectacular natural scenery and gives you an opportunity to witness the famous blue haze.
Heading roughly two and a half hours north from Sydney is Port Stephens, a beautiful port known for its resident dolphins and local fishing. Nelson Bay makes a lovely place to stay.
The Hunter Valley is also only a short drive away from both Sydney and Port Stephens. You really must visit, as the scenery and landscape is truly beautiful. The wines are also a good reason to go, as there are so many delicious wines to sample and buy.