Went to Brisbane a few years ago.
Loved the city. Decent little dowtown. They have this crab festival that happens every year.(can't remember when) You can also go to the tangalooma islands and swim with the dolphins in the dolphin sanctuary. You'll have a blast seeing the dolphins swim next to your boat.
You're also close to the gold coast and if you like beaches and sun and hot wommenz, hit up the gold coast.

 

^

You like dolphins?

 

Beaches, sun and lovely landscape . I'm going to see if I can fit Brisbane in my trip. I almost sure I choosing Sydney over Melbourne. About 575 miles from Sydney to Brisbane.

 

Sydney in April is getting coldish - low 20 odd degrees celsius, you'll suffer shrinkage if going for a swim. I'd go to Bondi for a visit to say you've been, wouldn't swim there - I'd go to Coogee or Manly.
Do a Bridge Climb (Harbour Bridge), really, really worth it - go during the day if you want great views, or at dusk so you can see the lights etc.
Do a jet boat ride around Sydney Harbour (get on at Darling Harbour - make sure you pack extra clothes or you'll look like you just pissed yourself/went for a swim in your clothes) - good for sightseeing as most of the dudes that take you tell you about the sights when your not hammering along doing 360's.
Go for a walk around The Rocks, Darling Harbour and up and down George and Pitt St's.
Go to Tarongo Zoo, will use up a few hours and is pretty good.
Could go to Luna Park (North Sydney at the base of the Harbour Bridge) for some old school theme park fun.
If you hire a car for a day or 2 (or catch a train) go to the Blue Mountains - see the 3 sisters.

If you get some extra days somewhere, either go to Melbourne or Brisbane, look up local flights (Virgin Blue, Jetstar, Tiger) as you can sometimes get flights from Sydney for $20 one way.
Brisbane *should* have cheap accommodation due to the floods and trying to get the tourism industry back on its feet.
Can drive back down the coast about 45mins to the Gold Coast which is abit of a party place and ALOT of tourist stuff to do there (theme parks, beaches, lots of nightclubs etc etc).
No idea about Melbourne, been there once for a stop-over and didn't get to see much - they have trams...

It depends what you want to do thou - chill out or pack as much in as you can.

For cheap accommodation/deals etc, look at;
wotif.com.au
readyrooms.com.au
expedia.com.au
lastminute.com.au
quickbeds.com.au

 

I have this free "The Official Guide: Sydney" book I picked up from Sydney Airport when I visited there in 2009. You can have it if you want (PM me) but you have to meet me in South SF.

 

YES! Im in Daly City and very close to SSF. PM sent!

 

I have been to Sydney, but for only three days. It was an awesome place and would like to go back. Kings Cross had some chill bars, the aquarium was nice, got a tour of the opera house which was awesome. The people there are extremely friendly and I made friends easily. Hung out with one girl who took me to a couple bars (don't really remember what area, but I think it was downtown). Have fun!

 

Fam lives in Gold Coast. they said hit up Sydney.