Streets Beach at South Bank is fantastic for kids - they have a really cool fountain and water course area for little ones and a lap pool surrounded by palm trees, with Lifeguards on duty and a perfect view of the CBD and Brisbane River.
Chermside has a great water park suitable for the very youngest through to teenagers while adults can get a few laps in the main pool.
Around Brisbane there are plenty of natural places to go swimming. Such as , Lower Portals, Mt Barney, Gwongoorool pool, Binna Burra, Noosa Heads for swimming on the beach, Cedar Creek Falls Rock Pools at Tamborine and Kondalilla Falls.
I agree with Lucy. Street's Beach in Southbank Parklands is great for kids. There are several pools from which to choose. Enjoy a lovely white sandy beach. It's really close to Brisbane city, there are Life Guards and it is free.