Stuff-all to do on Horny Island. Maybe stay in the Wondai Motel, and take a ferry trip over to Thursday Island to see the museum, get a coffee (nothing drinkable on Horn), watch the underwater geckos drifting along as the tidal rush goes by. A beer will cost $7++ so try not to be thirsty.
At Weipa, the Albatross Motel used to be OK but the last time I stayed there was 1976, so perhaps things have changed....