What to do?

It really depends how much time you have to spare & what you like to do on holidays.

For those not scared of heights a walk over the the bridge is one way to see Sydney from way up high - be warned, it's not for the faint hearted but well worth it. http://www.bridgeclimb.com.au/?mt_typ=9300&source=aw_sydney_bridgeclimb

Heights a bit to much? How about keeping it a harbour level & catching the ferry from Circular Quay to spend an afternoon in Manly? Or catch the ferry to Mosman and spend the afternoon at Taronga Zoo http://www.zoo.nsw.gov.au/content/view.asp?id=39.

The Bondi to Coogee walk. http://www.about-australia.com/travel-guides/new-south-wales/sydney/attractions/natural/bondi-to-coogee-coastal-walk/wales/sydney/attractions/natural/bondi-to-coogee-coastal-walk/ It takes about two hours on a cemented path & impossible to get lost. You don't need to be fit to walk it although do expect to be run down by joggers for most of the way. Take a hat & sun screen - no shade for the journey.

If you want to give your credit card a good going over, the Westfield shopping centre at Bondi Junction http://westfield.com/bondijunction/index.html combined with the shops along Oxford Street, Paddington should satisfy most retail cravings. Talking about Paddington, there are fantastic Saturday markets held in the grounds of Paddington Uniting Church http://www.paddingtonmarkets.com.au/.

For those interested in Sydney's convict history, The Rocks is an interesting place to visit http://www.therocks.com/are.

The Botanical Gardens http://www.rbgsyd.nsw.gov.au/ back onto the Opera House & arereally lovely to walk around. The view of the bridge from Lady Macquaries chair is worth a visit, particularly at sunset.

Day trips from Sydney
For those keen to escape to clutches of the city, the Blue Mountains is the perfect place to get away for a day http://www.bluemts.com.au/. A round trip is do-able in a day and keep in mind that it is usually 3-4 degrees cooler than Sydney.
For those wanting more than just a day trip, the Hunter Valley (4 hours north of Sydney) is a great place to visit if you are keen on Australian wines. As the centre of NSW wine country, it makes for a great place for an overnight stay. http://www.winecountry.com.au/