Welcome! The airports around are Bankstown (horrible place - think of Archerfield), Hoxton Park (closing in 2008), Camden (my favourite), The Oaks (RA airfield, near Camden), Wedderburn (getting further away now), and if you head north to the Central Coast there is Somersby (RA - trikes?) and Warnervale (which is also closing, not sure when).
Bankstown is a GAAP, parallel runways, unfriendly. Hoxton is a CTAF with one sealed runway. GA, helicopters. The Oaks is a grass RA airfield, CTAF. Camden has one sealed runway and a grass cross strip. GAAP on weekends, CTAF during the week. GA, gliders, lots of interesting aircraft, friendly and a pretty place. Somersby has a pretty awful strip. CTAF.
My suggestion would be to go out and have a look around before making your decision. Look at the airports, talk to people, look at the aircraft. You could easily visit Bankstown (if you want to), Hoxton, Camden and The Oaks in a day. Sometimes I find that talking on the phone is not the same as getting a feel for the place yourself.
This weekend should be a good one - why not pop out and have a look?