Where should we stay?

Mossman. Great butcher at the end of town near a hardware store. In a back street there is a self serve BP depot with much cheaper fuel.

You have a few options really.Mossman is my hometown so I'm likely to be a bit biased but the Riverside Caravan Park on the banks of the Mossman River is pretty good and is just 1km north of town and about 5km from the Mossman Gorge. To the south of Mossman and still north of Cairns you have Ellis Beach (caravan park on the Cook Highway and right on the beach), a Big 4 near the Mowbray turnoff just to the south of Port Douglas and then there is another park in Port Douglas proper. To the north of Mossman there is another beachside park at Newell Beach (about 4km from Mossman) and a little further north at Wonga Beach there is the Pinnacles caravan park (about 10-12km north of Mossman). There's anther park in Daintree and there bush camping is available from Noah Beach across the Daintree River on the Cape Tribulation road. All of these are pretty good options but if you want to spend some quality time at the Mossman Gorge then I'd recommend the park on the Mossman River. Links provided where appropriate.

While there has been talk of establishing a camping area in the Mossman Gorge precinct I don't believe that has happened yet.