If you get tired of the city, take a day trip out to the Blue Mountains, a UNESCO World Heritage Site named for the blue haze that surrounds the range. Echo Point is popular cliff lookout because it provides a great view a set of sandstone peaks called the Three Sisters. Arrive early to avoid the crowds. Take one of the many bushwalks (hiking trails) through the area and be sure to visit Wentworth falls.
The mountains are a 90-minute drive from the city. For those traveling solo or without a car, the area can be reached by train. At the Katoomba Station, purchase a ticket for The Blue Mountains ExplorerLink bus that allows you to hop-on and hop-off at various destinations.