Outside the city
Sydney is a big, sprawling city, and it can take hours to get out of it, particularly if you avoid the toll ways. But the city is worth escaping, as wonderful as it is, because much of the country around Sydney being on the more gorgeous side of gorgeous. NSW is surely one of world's more geographically blessed regions.
To the south of Sydney lies the imaginatively titled South Coast, which is dotted with small towns - mostly picturesque - along with rolling farming country, and lots of pretty beaches. The major center is Wollongong, an old steel town (though most of its factories are closed now). If you are looking for a pretty little town filled to bursting with cute cafes and craft stores, try Berry; while good beaches are found, for instance, at Gerringong – though most beaches around these parts are both pretty and relatively unspoilt.
To the North of Sydney lies the Hawkesbury/Pittwater, a strikingly beautiful riverine estuary. If you have a chance, see it by boat; if not, you'll see it from the train window, and there are good views from the highway as well. Further along the coast is the Central Coast, an area of dull towns not really worth visiting, unless you have a relative who lives there or something. Head further north, however, and you will discover the glories of the mid-North Coast. Some of the beaches in the area of Forster-Tuncurry are simply astonishingly beautiful. Try, for instance, Blueys Beach. You'll need a car to get there, but if you have the time and money, stay a week. You'll remember it forever.
Heading inland, you'll find the Blue Mountains, home to Katoomba, Sydney's grooviest, most laidback neighbor, and capital of the Blue Mountains region. Katoomba it makes a good base for the area, while further inland is Blackheath, a similarly laid-back, but somewhat smaller, village. The Blue Mountains area has much of Sydney's best walking, and is home to the glorious Three Sisters, vast monolithic outcrops overlooking a deep valley, the Jamison. The view is stunning and worth the trip. There are also a number of organized tours of various durations that depart for the area from central Sydney.