I will have 2.5 days to visit Daintree National Park from Cairns (and get back there). What are the possible itineraries to do it as a backpacker (and keep the costs down)? I have seen many tours organized from Cairns, but they are rather expensive and I don't usually enjoy this kind of experience anyway - its nice to be able to decide for yourself! Is it worth hiring a car (for 1 or 2 people, not sure yet), or public transport is sufficient?
About five years ago I hired a car from Cairns and drove to the Daintree as you suggest. It is easy and scenic drive. A ferry crossing is included. This way you can find your own accommodation and easily get around if you want to hike, day-trip to the reef and generally explore.
I have not investigated public transport; there might be a bus service. You would likely need to catch taxis once there if you do arrive by bus.