If you're travelling with kids, I definitely recommend basing yourself around South Bank, where there are so many child friendly activities and easy access to the city, cafes, parks, river, museums and galleries. Have fun and enjoy Brisbane!
Sofitel above Central Station has the reputation as the 4 star hotel of choice for people visiting Brisbane with great restaurants and other typical 5 star service.
There are also several river from 5 and park frontage 5 star hotels such as the Royal on Park.
The Regis is one of the better next tier hotels in the city. A little outside the CBD proper it provides river views and easy access to Roma Street Station which is more central for buses and trains than Central Station. It is also the main location for intercity trains and buses.
For great boutique hotels try Kangaroo Point, such as Il Mondo Boutique Hotel.
For the better motels friends have stayed at St Lucia, which has a number of hotels near the University of Queensland that are reasonably priced and give you plenty of options of public transport including the Ferry from the University.
Toowong also has a number of central choices.
For backpackers there are several options. Obviously the Valley is party central and stay there is you want to party first and sleep second.
Near the city are places such Chill Backpackers which is a popular choice.
Believe it or not, you don't have to leave Brisbane to find a good country style Bed & Breakfast hotel. Chapel Woods Bed and Breakfast is at the foot of the Honeyeater track up Mt Coot-tha is you are the type who wants to walk (or job) up a mountain early in the morning and perhaps see the sunrise.