gaxal
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This is a photo of a different hotel. What I described is the Pitsunda resort; here is its website with photos and other information.
http://kurort-pitsunda.ru/
However, it might be cool there in November. There is no pool, and the sea is probably around 12-14 degrees Celsius right now. The transfer from the airport takes about 2-3 hours if there is no queue at the border and costs 400-500 rubles by minibus, or 200 if you take a bus to the border.