Mentes

I am Mentes, son of wise Anchialos, and I rule over the Taphians, lovers of the oar. Now, as you see, I have come with a ship and my companions, sailing on the wine-dark sea to men of foreign speech, to Temesa after copper, and I bring shining iron. My ship is beached far from the city in a field, near the harbour of Rheithron beneath wooded Neion

He visits Telemachos' house, but he doesn't simply sail to the city harbour, instead he beaches his ship far from the city, which we can safely assume is to await a favourable wind for his voyage.

From this we can deduce the city harbour must not have been handy for an easy departure by the easterly winds Mentes would need.

As the city is also located 'beneath wooded Neion', but as Mentes has said they're nowhere near each other, we can conclude they must be located on opposite sides of the mountain.

This means we're looking for a mountain with a city on one side and a beach with fields suitable for departure by an easterly wind on the other. Also, according to Mentes, near a harbour called Rheithron.

Clearly, for it to be on the route from Taphos to Italy it can only be on the southern coast of Lefkada (our Ithaca), so it'd make sense to start our search there.

Temesa

Ithaca

Routes from Ithaca to Temesa

Among the suitors that have arrived, Telemachos discovers a stranger called Mentes. He tells Telemachos what he's doing in Ithaca:

Taphos

Kastos

Kalamos

Ithaca

Meganisi

Aigilips

Samos

Odussey Book 1 line 168-174 Barry B Powell

Ancient Taphos is believed to be the isle of Meganisi, close to the south-east coast of Lefkada. Neighbouring Kalamos and Kastos could also be part of that group.

From there Mentes is on his way to Temesa on the west coast of Italy and therefore has to cross the Ionean sea and pass the strait of Messina between Sicily and Italy, though as suggested in a paper by Michael Siebert (link 'Temesa'), initially the route would've been a direct cross-over, as the crow flies, to the east coast of Italy.