You could try Cala Fornells in Menorca for a mooring. The buses run to Mahon several times a day and then by taxi to airport. However, if you are unsuccessful in finding one there is not really anywhere near to go as Mahon is always full and, in my experience, particularly unsympathetic.

The sad fact of life is that this is a very crowded part of the Med and ALL facilities are at a premium. It gets worse in July and August when even picking up a tank of water becomes a major challenge.

Good luck.