One of the best places to bring the children to is the Queensland Cultural Centre which has the Queensland Museum and the Sciencentre which has great hands-on activities for them to be pre-occupied for hours. Another great place is Hands On Art (07 3876 5077, www.handsonart.org.au 150 Enoggera Terrace) which is a non-for-profit organization that arranges all sorts of art workshops for kids with clay modeling, painting, dancing and more. Bookings are essential so always check for availability. The Roma St Parkland is great if you want to get your children outdoors, as is the South Bank Parklands.
There are also babysitting services here in Brisbane:
Dial an Angel
Phone: 1300 721 111
Phone: (07) 38797455