Brisbane is a river town. There's no better way to view the city and suburbs the same way the first explorers did--by boat. The Brisbane City CityCat is a ferry service running the length of the river from Hamilton to St Lucia. Services run every thirty minutes for a two trip.
Queensland Rail is the State's train services, with all suburban and inter-urban services passing through or terminating at Central Station. Within a hours train ride you can visit the Railway Museum, The Australian Woolshed, Steve Irwin's famous Australia Zoo--or connect with a bus to the beaches of the Gold Coast or the Sunshine Coast.
With access to a car your choices to the west widen. Toowoomba--the City of Flowers, the Jondaryan Woolshed, Queensland Raceway, or the beauty of the Brisbane Valley with Somerset Dam and Wivenhoe Dam.
The inner city itself is a trove of adventure on a walking tour. The Queen Street Mall, the Maritime Museum, Southbank, the XXXX brewery and the Botanical Gardens are all within a 15 minute walk of most of the inner city accommodation.