Even though the vacancy rate is increasing in Brisbane, many of the good apartments for rent are hard to find. Often, this is because the existing tenant does not leave, and when they do become available, are snapped up quickly. For the better buildings, a large percentage of the apartments are occupied by the owner, and so are not rented out. 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 fed the better apartments.
At one time, a good specialist website for apartments was http://www.seqrents.com.au However, it seems that some buildings are not using this site anymore, or are not bothering to update their listing on this site. So, although useful, it is less useful.
The largest number of listings are located on RealEstate.com.au, but a number of onsite managers do not use this website.
You have to find out how each manager advertises his/her vacancy.
Generally, you want to avoid any buildings managed by Oaks, as they focus on short term hotel style rentals.
Also, look at the posts and links on this blog. This website has a list of most city apartment buildings, with useful information and links about them. Also, try this customized search engine.
Inner City Brisbane:
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. The best thing to do here is call, because the website is not updated regularly. Telephone 07 3305 2559
If you want to live downtown, then I recommend the Admiralty Precinct. This comprises three first-tier buildings (Admiralty One, Admiralty Two and Admiralty Quays), plus River Place (good location, not as good quality) and Skyline (second tier).
Admiralty One is good value, and has some of the largest two bedroom apartments in Brisbane - http://www.admiraltyone.com.au/
Admiralty Two also has good sized apartments, and the building has great facilities. http://www.admiraltytwo.com.au/
Admiralty Quays is newer, and has a great pool, but the apartments are smaller. and it is more expensive. http://www.admiraltyquays.com/
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
Apartments in Suburbs
The suburbs that I recommend, due to location, transport and large number of better quality apartments, are Toowong, St Lucia, Taringa, Indooroopilly and possibly Milton and Hamilton. I don't recommend Chermside.
The newest complex in the Toowong / Taringa area is Fresh. This complex has two pools, a gym and great gardens. http://www.realestate.com.au/realestate/agent/acorn+realty+taringa/nrqhzu
Next door to Fresh is Encore, which is a relatively nice complex, with good pricing (but not as nice as Fresh, and some of the apartments are small). http://www.seqrents.com.au/encore/
St Lucia is harder to find quality -- there are few onsite managers. So you have to try local real estate agents, such as Ray White (who also has listings in Fresh).
In Indooroopilly, there has been recent construction, so there are a number of new, quality buildings. My two picks are Riva and Ciana.
Riva has apartments with great river views. It is a quiet building, with a pool, and is close to the train station and Indooroopilly Shopping Centre http://www.seqrents.com.au/riva/
Ciana is a larger new complex, in a central location, with many large apartments. There is a pool and gym, plus a bowls club! http://www.ciana.com.au/
If you want an apartment complex that feels more suburban, then Parklands at Sherwood is a great choice. Many apartments have park/rural views, and there is a great pool and bbq area http://www.centralsherwood.com.au/.
Nearby is Tennyson Reach, where you can get a large new apartment on the river. This is a new complex, but (apart from river views) not a great location.
This is a list by a selling agent about various inner city buildings: