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Цитата: The only flights I can find arrive at Krasnodar airport at 3.15am. What is public transport like at this time?

As far as I know public transport starts at 6-00.
Therefore, a taxi will get you to the hotel.

Цитата: What are some of the main attractions that you would recommend in Krasnodar?

I recommend you get to the street Postovaya. There to see the monument to Catherine 2, Alexander Nevsky Cathedral (in front of the monument), and then move up the street to the intersection Krasnaya and Babushkina.