The place being advertised as the best location is Oak Beach. It's also the starting point of the Solar Eclipse Marathon. However I wouldn't (and won't) go near here because the highway between Port Douglas and Cairns is one lane in each direction for most of it without alternate routes, and Oak Beach sits right on it.
Both Cairns and Port Douglas are well within the limits of the eclipse's path of totality according to the map on this site, and chances are you'll be staying at either of those so I would suggest staying put or, at most, heading up to one of Cairns' northern beaches. From what I understand of eclipses, as long as you're within the path of totality you will have an equivalent experience of anyone else within the path barring clouds, etc.
If you really want to sit on the central line of the eclipse I'd suggest figuring out where it's going to pass over the road between Mt Molloy and Mossman and pull up on the side of the road there. It may be occupied but it should be a lot quieter than Oak Beach. By my calculations it should be close enough to the Julatten pub that I'd just head there and hope they were open at 5 am. ;)
If there's cloud anywhere along the coast, chances are there will be cloud all along the coast so one place won't be better than another in that regard. Heading inland to the Mareeba to Mount Molloy area will be more likely to get you clear skies as that area is a lot drier, if that plays into your figures.
Personally I'll either be sitting at home with a beer or heading down to one of Cairns's beaches (not the Esplanade as I expect that to be very crowded too) with a beer. Just not XXXX.