Planning Your Time
It's wise to decide in advance whether you'd like to cover a lot of ground quickly or choose one or two places to linger a while. If you have less than four days, stick close to Sydney. In a busy four- to seven-day period you could visit the Blue Mountains and the Hunter Valley as well.
Start with a visit to the Blue Mountains. You could arrange a round-trip itinerary from Sydney in a fairly hectic day or, preferably, spend a night in Katoomba, Blackheath, or Leura and make it a two-day excursion. Return to Sydney, and then head north to the Hunter Valley. A two-day/one-night driving visit here allows you enough time to see the main sights and spend time touring the wineries before traveling back to Sydney on the second day. An alternative would be a quick visit to the Blue Mountains, then two days in Canberra to see the city's excellent museums and galleries.
If you have more time in the region, continue to the North Coast. In three days of driving you won’t likely get much farther than Coffs Harbour (with overnights there and in Port Macquarie), and this requires rushing it, but it's possible to fly back to Sydney from Coffs. Alternatively, travel southwest to sedate Canberra and have a leisurely few days exploring gems like the National Portrait Gallery, Parliament House, and the Australian War Memorial, while stretching your legs walking or biking around Lake Burley Griffin.