Re free camping: 30km south of Cairns is the iconic Gordonvale Rest Area, where camping is allowed. I have spent many a memorable night there, once when they were burning the cane field just next to it. Here’s a link – http://deanwormald.com/australia-vanroad-trip/free-camping-at-gordonvale-near-cairns/. I can’t vouch for the info in the link, but it was the one that popped up when I googled.

Queensland has quite a few of these free camping rest areas with toilets and showers. There used to be a map put out by RACQ.

Bon voyage!

PS, the rest area showers are cold water but wonderfully refreshing when you’ve been living like a feral!

Daintree walks and hiking trails.
http://daintree.info/ifwalks.html
Camping in the Daintree
http://www.daintreecoast.com/acc_list.ph…

Overnight I suggest Henrietta Creek. This is located on the Palmerston Highway between Millaa Millaa and Innisfail in the Wet Tropics. On the highway but not much traffic at night but in a rainforested location. The 6km round trip walk from Henrietta Creek to Nandroya Falls and past Silver Falls is magnificent, and also some chance of platypus spotting in the goologan creek dawn or dusk. Nandroya Trail head is over the other side of the creek form the camp spot at the end of the grassy area.Then other walks to other falls as well from the campsite as well. Best camping.walking combo in the region. About $5 to camp I think, not much.

This would be the best result for your request.

http://www.wettropics.gov.au/ttd/tdd_palmerston_parks.html

Nearby MaMu rainforest canopy walk – about $20.
http://www.derm.qld.gov.au/parks/mamu/index.html

Also along the way stop for some yoghurt at Mungalli Creek cafe –

Then go down to Innisfail and drive back to Cairns along the highway and stop at Josephine Falls. Go this direction as easier driving up the Gillies and down the Plamerston.

And/or

Drive north and park at Ellis beach campground and then drive to Mossman Gorge the following morning, about 1/2 hour but very scenic drive.. It is about $30 a night as oceanfront.
http://www.ellisbeach.com/camp.php

Maps
http://www.cairns.com.au/visitor-information/cairns-maps.html

edit. Mission beach hit hard with cyclone damge and forests not recovered yet.
Cape Tribulation is not great for hikes, mainly boardwalks. Nice place to stay though.

1…It’s the largest living coral reef in the world …over 2,000km of living coral with an amazing variety of marine life …

2…It provides a natural protective barrier for the coastline..

http://www.gbrmpa.gov.au/

http://www.aims.gov.au/

http://www.csiro.au/science/Oceans.html

http://www.abc.net.au/science/tag/browse.htm?topic=enviro&tag=oceans-and-reefs

Cairns & anywhere in the tropics is always hot , wet & humid at that time of year …

Here’s a site that gives average weather conditions throughout the year..

http://www.cairns-australia.com/cairns-weather.html