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Brisbane = 1 track at Chandler. Built for 1982 Commonwealth Games. 330m, concrete, outdoor. bring a MTB.

Nerang = 1 hour south of Bris. Bitumen, back straight uphill. Bring a MTB.

Caboolture = 30 min north of Bris. See Nerang, but not so uphill..... Bring a MTB.

Ipswich = 1 hr west of Bris.
Toowoomba = 2 hrs west of Bris.
Warwick =3 hrs west of Bris.

 .......... Bring a MTB.  OK, so you could probably get away with a hybrid at Toowoomba.

There is one really nice track just south of Brissy though. Couple hours drive, scenic. Good surfing on the way. Little town called Sydney.

Seriously, all are ridable. None are great.
Need to contact http://www.qld.cycling.org.au/ to book Chandler, probably.
Not sure if Ipswich or Toowoomba still in use, but probably on both counts.

Ipswich has a pretty nice BMX track too. I've got family there. Its not a bad place despite what ppl in Brisneyland may say.