The best price found from United States to Odesa is on August 6th, 2019, travelling with Alaska Airlines. See more options, compare prices and book: search flights.
The old and the new terminals of Odesa airport stand 200m apart. The old one, a shabby Soviet affair, was still handling departures at the time of research. The slick new terminal only processed arrivals.
The airport is about 12km southwest of the city centre, off Ovidiopilska doroha. Trolleybus 14 connects it with the train station. The infrequent bus 117 goes to the centre, stopping at Pl Hretska Bus Stop.
Odesa is better linked to Europe than any other Ukrainian city, with the exception of Kyiv. Austrian Airlines, LOT, Air Baltic, Czech Airlines and Turkish Airlines all have regular flights to Odesa, and various regional carriers fly to former Soviet countries. The Ukrainian airline UIA (MAU) has flights from Odesa to Istanbul and Tel Aviv.
UIA and Motor Sich fly between Odesa and Kyiv at least four times daily. Kiy Avia can sort you out with tickets and timetables. Sadly, there are no flights elsewhere around Ukraine.