Best Greek islands to visit in October
Tough question! Each island is different and it's difficult to vote for the "best" ones. In addition, I don't think there more than 100 living persons that have actually been to all of them to be really able to compare them (~6000 islands from which the 117 are inhabited).
Nevertheless, I'll try to share my opinion taking into account the preferences that you've listed. I've been to a lot of them but mostly in summer (June-August). Greek islands are much different during winter, and in my opinion more beautiful (even if you lose all the action, the sun, the snorkeling etc). Please note also that in November, there's no partying in any Greek island and most probably you will be cut from most tours and historic sites.
- The ones with the most available choices at this season, are the biggest ones, with enough local population to make keeping the businesses open worthwhile. Crete, Rhodes, Corfu/Kerkyra. In Crete you will never get bored, there are many things to do and visit. Great archeological sites. Amazing food. Airplane is a real option. It's in the south, you will get the best weather possible ATM in Greece. On the other hand, you won't get a feeling that you are actually in an island, has similarities to the mainland. As with all these 3 islands, it's way too big, you will have to rent a car. Rhodes is a very beautiful city, with a nice medieval flavour that you won't experience anywhere else in Greece. Most businesses will be open, because the city has a university and therefore a vivid life. A lot of different landscapes to explore. You are in the Dodecanese, so you can easily jump into a ferry a visit in a few hours a nearby remote island for a couple of days. Corfu is another island with fortifications made by the Venetians. Nice city, quite touristic during summer with a lot of Italians visiting.
- Go to the close ones to you, in the Ionian sea. Zante/Zakynthos, Kefalonia and Lefkada are big enough to have all the necessary services. There's nothing to be afraid of, you won't be left alone in a deserted island :) IMO Kefalonia and Lefkada have nice nature too. Zante unfortunately the last decades has been more prone to self-destruction in the name of quick profit.
- Go to the Cyclades. Very different style from all the aforementioned islands. Usually the main village (called "Χώρα"="Chora" which can be literally translated as "country") is a picturesque village with narrow sidewalks and little white-blue houses as you have probably seen in movies or in advertisements. Santorini, Mykonos, Sifnos, are all big enough and well known to have a decent amount of things to do even during winter. Santorini has a volcano, amazing scenery, but be careful, it might be more expensive compared to the other options.