South Bank - Brisbane's only beach (artifical, but nicely done) is right in the heart of the city in the cultural district, surrounded by lots of interesting shops, cafes and restaurants (which can be slightly expensive) as well as some of the city's museums, theatres and art gallery. A great place to hang out on a hot day and have a swim (for free). South Bank Parklands ( http://www.south-bank.net.au/ )
The Maritime Museum's destroyer can be seen docked in the lower right-hand corner of the image. The large white-roofed building is the Brisbane Convention Centre.
Suncorp Piazza found within Southbank often hosts free live events and movies.
Brisbane City Hall and King George Square - located between Adelaide and Ann Streets, this is the city's most significant historical landmark. City Hall often hosts free concerts throughout the year. There is a restored lift that can be taken to the top of the clock tower for free.
Mt Coot-tha - Brisbane's tallest mountain. A popular makeout spot with a great view and good but overpriced cafe and restaurant. Also home to the one of the Botanical Gardens.
Manly Boat Harbour - at Manly, the second largest in the southern hemisphere. There is also a public park located at Norfolk Point.
New Farm Park - large park on the river in New Farm.
CityCat - Take the CityCat river taxis up and down the river. A great couple of hours to see the city at speed - secure your sunglasses and hats though.
Brisbane City Council has a large list of recreation facilities available in Brisbane on their website: Recreation Facilities in Brisbane