Hey gossy,
I second Lamington NP (both Binna Burra and O'Reilly's are great, though you'll come across loads more people at O'Reilly's as its a popular tourist spot). Both are 1.5-2 hours drive from Brisbane. If you are into rainforest and waterfalls, Lamington has several good options. I recently did Toolona Creek circuit at O'Reilly's and thought it was awesome (some photos are on my blog here:
http://sirkingchampionmunch.blogspot.co ... rcuit.html). Shipstern as suggested is good also, if you like varied vegetation + lots of views + one big waterfall.
If the weather is fine and you prefer hiking up a mountain (and getting unobstructed views from the top), there are several good options in Mt Barney NP. Again you're looking at 1.5-2 hours drive. Mt Barney itself is a very long and challenging day depending on the fitness of your group, but Mt May or Mt Maroon are shorter options (although I haven't done either walk before, there are numerous trip reports on the web).
West is Main Range NP, again some great rainforest walks with good views. Within 2 hours' drive you can visit Cunningham's Gap (Mt Mitchell or Mt Cordeaux are great walks) or Spicer's Gap (Mt Mathieson Circuit/Governor's Chair Lookout for awesome views).
North there is glasshouse mountains as suggested, about an hour drive. You get a nice view from the top of Mt Ngungun (short walk with some easy scrambling sections) but the two other popular options Mts Tibrogargan and Beerwah are currently closed. Another hour further north you could do some nice beach hiking at Noosa NP or Cooloola NP.
For something closer to the city, D'Aguilar NP has a nice selection of short, easy walks (see:
http://www.nprsr.qld.gov.au/parks/daguilar/). Greene's Falls/Rainforest circuit is probably the pick of the bunch, but you can combine several to make a longer day of it. There are nice picnic areas here if you fancy a barbeque. It's also a nice drive up through here to Mt Nebo or Mt Glorious but on weekends you have to contend with multitidues of cyclists and motorcyclists.
In short, there are many, many options for hiking around Brisbane. Just depends on what kind of walk you're keen on and how much time you have to spare.

Cheers,
Munch