Venice Marco Polo Airport: The sensible gateway. Take the direct Cortina Express coach from the airport to Cortina bus station: roughly 2.5–3 hours, about €30–40 one way. Book ahead in ski season, July–August, and around major events; it includes normal luggage and ski/snowboard carriage. Do not detour via Venice’s rail stations unless the direct coach timetable does not work.
Treviso Airport: Only choose Treviso if the flight saving is substantial. Cortina Express serves Treviso, but its stop is not at the airport: allow about 30 minutes and one or two local-bus connections to reach it. The onward coach is roughly 2.5–3 hours. Venice Marco Polo is much cleaner operationally.
Innsbruck Airport: A viable flight airport on a map, but not a good independent-transfer airport: there is no straightforward scheduled coach to Cortina. Unless a package includes the transfer or you are hiring a car, skip it; a private taxi is expensive and the journey is roughly 2.5–3 hours depending on conditions.
Calalzo-Pieve di Cadore-Cortina railway station: The useful rail approach from Venice. Trains from Venice reach Calalzo in about 2 hours 45 minutes; connect to a Dolomiti Bus shortly after arrival for Cortina, around 30 minutes. The train fare cited locally is about €7.50 and the bus about €3, but check the seasonal timetable and connection before committing. A taxi is about €65, so save it for a missed connection or a group.
Toblach/Dobbiaco railway station: The northern rail gateway, useful from South Tyrol or Austria: regional trains stop at Toblach and SAD buses cover the 31 km to Cortina. Allow roughly an hour for the bus, plus a buffer—services are not urban-frequency transport.