Local parks are great for an impromptu picnic after school or work. My family is fortunate to live near two fabulous parks: C B Mott Park and Glindemann Park. Both parks have excellent barbecue facilities, ample shade, and interesting playgrounds for the kids.
Kangaroo Point Cliffs is a special spot with spectacular views; popular with couples on romantic (and inexpensive) dinner dates.
The Lota Camping Ground Reserve on the Esplanade at Lota on the Bayside would be my pick. The area has been recently upgraded by the BCC. There are excellent BBQ and shelter facilities. There is an excellent play area for the kids as well as an exercise area for the older kids. The views of Moreton Bay across to Wellington Point are awesome and if the tide is high, you can cast a line. Bring a few bikes as the Moreton Bay Cycleway (MBC) runs through the reserve and you can ride to Wynnum North along the foreshore. Alternatively a short stroll to the north brings you to Manly Harbour, the village of Manly (with its coffee shops and restaurants) and if you are on a weekend, Jan Powers Farmers Markets on the Manly foreshore.
Roma Street Parklands provides a range of venues. This meandering park has many quiet alcoves and barbecue areas where you can have a picnic or places where you can host a party for hundreds if you like. The sport fields give you plenty opportunity to be active during your picnic.
There is plenty of parking and access by bus and rail.
The best thing is that it is one of the few parks in Brisbane where it is legal to drink.
Lower Moora Park at Park Parade, SHORNCLIFFE. Fantastic huge playground, beach, swimming, building sandcastles, fishing on the jetty, long flat bike track, lots of bbq's & tables with heaps of shady spots, toilets, fish & chip shop near by on the top of the hill.