New Farm Park - just a short river cat ride from the CBD. Has the biggest rose garden in the Southern Hemisphere, beautiful old fig trees and a great playground.  Plenty of lawns to stretch out and enjoy a picnic.

Roma Street Parklands - A fantastic spot in the heart of the city to relax.  With 42 acres of manicured gardens, walking paths, playgrounds to suit all ages, lakes, bbq's and shelters.  The lake is not fenced however there is plenty of room to picnic away from water.  Guided walks of the gardens are available and there is a train the kids can ride on (check timetables). They offer special guided tours for Parents and Bubs every Wednesday at 11am leaving the Cafe. Events are held from time to time in the amphitheatre or on the lawns.  Entry is free. For more details contact 07 30064545

South Bank lagoon and recreational area - walkways and bikepaths run along the river in the heart of the city.  There is so much to offer everyone here, from restuarants, free activities on Saturdays (eg yoga), great playgrounds, markets and entertainment.  The highlight for families would have to be the stunning lagoon style pool (not fenced)that stretches out along the river.  The depth varies to suit all ages and in summer a life saver is often on duty. Plenty of picnic and bbq facilities and shade, this place is family paradise in a city.  Entry is free.

Ipswich

Ipswich's Queens Park has just undergone Stage 1 of a major transformation.  It now has a great range of child-friendly activities including a flying-fox, water pumps, climbing equipment and other great things.  There are public BBQ's, toilets and a kiosk. 
Queen's Park playground adjoins the Queens Park nature Centre, where you and your family can wander along the boardwalk and see many species of native animals, a superb bird aviary and finish in the animal nursery. 
After that, you can visit  Nerima Gardens, the wonderous Japanese gardens also within Queens Park.  Stage 2 of these gardens have recently opened and they are a peaceful way to end an energetic day with the kids. 
Queens Park has been developed for years so it is very well shaded by old trees, and has lots of grassed area for picnics. 
You could spend a whole day out at Queens Park Ipswich, so come and see for yourself.  Thanks to G.W Qld