I have friends who have been to queenstown - and said it is a blast. Bungee jumping, jet boating on tiny creeks, white water rafting etc. - lots of stuff to do there apart from skiing.
Would you be interested in canyoning /abseiling kinda stuff. If so, have a look at this:
http://www.canyontours.com.au/
On Ella's Uluru suggestion - Ella, have driven down from Alice? it is a F'ing long drive - about 8 hours round trip - especially when you can fly direct into Uluru itself. It is a great place to go - but I would suggest going out to The olgas as well (aboriginal name of Katajuta sp??) and take a walk through the valley of the winds - IMHO, more spectacular than Uluru.
Places to stay in Sydney - there are so many hotels - I would suggest (depending on your budget) trying to stay at somewhere that has a view (either over darling harbour) or circular quay/opera house. I have stayed in the Shangri-La (even if not staying here, worth a look at the cocktail bar on the top floor - pretty nice view - though the cocktails are rather pricey) which is really nice, and the almost floor to ceiling windows overlooking the harbour are fantastic (though it is kinda at the pricey end of hotels). I nearly always book my hotel accomodation online (
www.wotif.com) have a good selection of sydney accomodation - but only 2 weeks in advance...
Things to do in Sydney:
If you are techy minded, the powerhouse museum is pretty interesting.
Take a ferry trip to Manly or a harbour cruise.
Historical (I know Oz isn't that old but) a walk around the Rocks is pretty interesting.
Also the Botanic gardens and Mrs Macquaries chair is easy walkable distance around passed the opera house - this is where the colony really started!!
Pubs - take a walk to the Lord Nelson (on Kent St) and try some of the house beers! The old Admiral's has a kick like a mule
Also worth seeing is the Hero of Waterloo and the Mercantile (good old irish pub) - this place goes off on a saturday night. These are all in the Rocks.
Blue mountains walks - there are great views from so many places - but I particularly like the walk from the (Wentworth Falls) train station / highway following the creek to Wentworth Falls itself. It is a pretty easy (and flat walk) but crosses the creek right at the top of the falls and continues down into the valley - must admit that I haven't gone too far down here, but even going down a little way gives a spectacular view back onto the falls themselves.