The Amorgos Island is also like almost all the Cyclades Islands, beaten by sometimes strong winds which, in addition to being annoying when you are on the beach, can also be dangerous if you do not drive a suitable vehicle.
Having said that, you will have already guessed that the scooter is only for expert motorcyclists and that it would be good to rent a cylinder capacity not below 150 cc. but in addition to the weather factor, it must be emphasized that the roads are almost all in the mountains given the morphology of the island with breathtaking views but very exposed to the winds. Let's also add climbs, various hairpin bends and little goats that suddenly appear as if by magic and you understand by yourself that it becomes quite dangerous and difficult. Duclis in fundo Amorgos from north to south is about fifty kilometers away and we have told you everything!
The car remains the most appropriate solution according to our point of view for a matter of comfort and safety. On the contrary, it is inconvenient to park as there are very few spaces to put the vehicle in and therefore you may even have to walk a little way to reach your destination.
For quad lovers, unfortunately there are few dirt roads where you can also have fun driving but this does not mean that it cannot be an excellent alternative, the choice is yours ...
Finally, for those who are patient and have no intention of driving any type of vehicle, there are public bus routes which, especially in the summer period, also have routes in the late evening so as to be able to organize perhaps even a dinner away from your point base and for those arriving by ferry in one of the two ports. Below the link where you can check the timetables and itineraries:
https://amorgosbuscompany.com/en/timetable/
Last option perhaps the simplest but also a bit more expensive is to travel by taxi. But let's say that there are very few of them, so much so that the ideal would be to "share" the car with other travelers so as to amortize the costs. Prices more or less are around 8€ from Katapola to the Chora, while around 25€ to reach Aegiali from Katapola.