With regard to things being closed, I can only inform you about Rhodes but would expect Kos to be the same.
Whilst the out and out resorts are wrapped up in plastic at the end of October the rest of the island is open for business. The museums and outdoor sites are open all year round.
If you visit in November you will get the opportunity to tour the island and see it's beauty. There are many traditional villages which will give you a taste of real Greek life. I would recommend Afandou as a great central point to stay and there is accommodation available all year round.
Afandou is a traditional Greek village that has some tourism in the summer and therefore most of the bar and restaurant owners speak good English.
November in Rhodes can be unexpectedly warm with temperatures that can be in the low 20s, the sea is still warm enough to swim in and the beaches are empty.
I hope you make it to Rhodes.
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