There are absolutely thousands of places in and around Cooktown where you can plunk down and have a fantastic picnic, including one of the beaches or National Parks. You may prefer to plan your day, however, so here are a couple of options.
Campe Drive Picnic Area
Campe Drive Picnic Area is located at the end of Campe Drive approximately 2 kms south of Trevethan Creek crossing (Cooktown Development Road). The picnic area is on the banks of the Annan River just below the Cooktown water supply weir. Here it is safe to swim or try a little fishing.
Annan Gorge
After Black Mountain, Cooktown Developmental Road continues until you reach the "Little Annan" River bridge. This is a concrete span over the rocky bed of the Annan River. Just before crossing over the bridge, a track on the right leads to the Annan Gorge, where the river has cut its way through the granite over a waterfall. Across the bridge, on the left, there is a shaded picnic spot and safe, refreshing swimming. The fast, cool Annan waters pool briefly before cascading downstream to the stone walled beauty of Annan Gorge.
Cooktown Botanic Gardens
Cooktown's Botanic Gardens are located on Finch Bay Road. There are plenty of tables and picnic sites to choose from. While you're there, stop in at Nature's Powerhouse Interpretive Centre for more information, or just to have a look around.