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Many of the good apartments for rent are hard to find. Often, this is because they are snapped up quickly. Also, onsite managers often control the rental rolls, and don't often advertise on the usual property websites (as they don't need to do so). Some have their own website. Also, onsite managers may have a relationship with executive relocation services, that are feed the better apartments.
If you are looking for a place to rent a good inner city apartment, I believe that this is the best site to look at: http://www.seqrents.com.au
Also, try: http://www.raas.com.au
You have to find out how each manager advertises his/her vacancy. You want to avoid any buildings managed by Oaks, as they focus on short term hotel style rentals.
Some places to look:
I recommend Arbour on Grey at SouthBank: http://arbour.com.au/cms/welcome.html
Also, Saville at SouthBank is one of the nicest buildings if you get a river facing apartment: http://www.seqrents.com.au/saville/index.htm
I know people at LeftBank at West End who like living there, but it is a little bit far to walk to any shops -- it is in an industrial area: http://www.seqrents.com.au/leftbank/
In the city, Admiralty One, is good value - see prior posts: http://www.seqrents.com.au/admiralty/
Admiralty Quays and Admiralty Two are also good quality.
Nearby on the river in the city is River Place, that is not as good quality, but is likely to have availability as this is a large complex. Careful of Storey Bridge noise. Great views.
On Alice Street in the city, if you can get an apartment in Quay West, that is fantastic, as it has park and river views -- for long term rentals, the best agent to try is Blockside & Fergerson for this building. Half of this building is a hotel managed, so it is easy to get short term accommodation in Quay West. All apartments are privately owned. You want to get above level 7.
For an inner city downtown building, Metro 21 is one of the better quality buildings. It has only 4 apartments per floor -- and tries to be more upmarket so is better than most buildings that aim at students -- it seems to have better availability, and some of the two bedroom apartments have three bathrooms. The baloneys are large: http://www.realestate.com.au/realestate/agent/metro+21+brisbane/mlibri
In the back of Toowong, Encore is a relatively nice complex, with good pricing (but currently construction next door, so take care of which apartment). http://www.seqrents.com.au/encore/
St Lucia is harder to find quality -- there are few onsite managers.
In Indooroopilly, Riva is the only quality building -- again, some are noisy due to nearby construction. Some have river views. http://www.seqrents.com.au/riva/
This is a list by a selling agent about various innercity buildings: