Sochi International Airport is the best and the quickest way to get to Sochi. Air gateway is located in Adler district and it is a hi-tech and beautiful place with plenty of cafes, restaurants, shops and other facilities inside, even with modern artists' exhibitions.
Getting into town:
The cheapest way to get to the city is to leave the airport by bus or marshrutka 51, 105 and 105с to Adler and Sochi central railroad station and 135 to Krasnaya Polyana. It will cost 80 - 100Rbl and take you up to 35 minutes.
Taxi drivers at the airport will definitely offer you inadequate prices for a ride. To protect yourself, book taxi or transfer in advance or use taxi app. The most expensive ride (e.g. to Lazarevsky Sochi district) will cost approximately 3,500 - 4,000Rbl. A ride to Adler city will cost up to 800Rbl, to Central Sochi 1,000 - 1,500Rbl, and to Krasnaya Polyana 2,000 - 2,500Rbl.