Mentes route from Taphos

Meganisi

Ithaca

The route along the south coast of Ithaca

The routes represented by the yellow lines would require a more north-easterly wind in order to set sail and are more treacherous, because the ship is in greater danger of being pushed towards the rocky coasts. The green lines allow Mentes and his ship enough room to comfortably manoeuvre out of the harbour and, of course, around Capo Ducato.

Assuming Mentes would've beached in the most convenient place, we'll first take a look at those three green beaches to see if any fit the criteria and if we can also find a place that could be Rheithron.

Kalamos

Kastos

Capo Ducato

Taphians

As you can see from this picture Mentes' route from anywhere on the Taphian Islands (red lines) would pass Ithaca's south coast beaches, which I've marked with yellow and green dots. The yellow and green lines represent the routes Mentes would have to sail in the awaited easterly winds.