Since there are about 200 inhabited and visitable islands in Greece, it is difficult to make a choice.
However:
Rule N°1: Avoid the period between June 15 and September 15.
Rule N°2:
Avoid islands that have an airport. The more difficult they are to access (and only by ferry), the more they will be off the beaten track.
Rule N°3
Avoid islands that are too Instagrammed or are the subject of thousands of Youtube videos.
In the islands you mention, Ithaca is in the Ionian Islands, Patmos in the Dodecanese Islands.
The others are in the Cyclades islands.
Since these are completely different regions. It is best to first think in terms of groups of islands.
Also know that ferries don't go everywhere every day, and going directly from one island to another that seems very close can be impossible
And even doing this, be aware that Kea which is in the Cyclades is not accessible from the port of Piraeus but from the port of Lavrio which is less easy to reach from Athens while Kythnos located a few nautical miles away from Kea is accessible from the port of Piraeus.
Naxos is no longer an "off the beaten track" destination at all, it has become a major destination in the Cyclades with Paros, Milos to a lesser extent, and of course Mykonos and Santorini..
Tinos and Kythnos are still preserved from mass tourism.
Other islands such as for example Lemnos (North Aegean Sea) or Astypalea (between Cyclades and Dodecanese) or Folegandros (Cyclades) and many others are also off the beaten track.
