The administrative and commercial center for much of Cape York Peninsula is Cooktown , located in its far south-eastern corner . The peninsulaâ s largest settlement is the mining town Weipa on the Gulf of Carpentaria . The administrative and commercial center for much of Cape York Peninsula is Cooktown , located in its far south-eastern corner while the peninsulaâ s largest settlement is the mining town Weipa on the Gulf of Carpentaria .