Uzhhorod's airport currently has no flights, not even a domestic service to Kyiv.
There are long-distance buses to Lviv (186uah, five hours, up to 6 daily). Services also run to Rakhiv (144uah, around five hours, around 15 daily) and Mukacheve (28uah, one hour, every 15 to 20 minutes).
Marshrutky go to Chop (19uah, 50 minutes, around every 15 minutes) from the side of the bus station facing the train station. Cross-border buses link Uzhhorod most usefully with Košice (201uah, 2½ hours, six daily) in Slovakia. Regabus (www.regabus.cz) operates a daily overnight service to Prague (950uah, 12 hours).
Trains to and from central Europe don't stop in Uzhhorod; you must go to nearby Chop.
Domestic trains go to and from Lviv (120-300uah, six to nine hours, up to six daily) and Kyiv (200uah, 12 to 14½ hours, four daily). Other services include slow-but-scenic elektrychky (electric trains) to Mukacheve (14uah, 2½ hours, six daily) via Chop.
From Uzhhorod to Hungary & Slovakia
Chop, 23km south of Uzhhorod and 44km west of Mukacheve, is the international rail crossing between Ukraine and Hungary or Slovakia. Here, the broader Ukrainian rail gauge meets the narrower standard gauge of central Europe, and there's a delay of anything between one and three hours while your train's carriages are lifted in the air and onto different bogies.
Trains affected are long-distance services like the Lviv–Budapest or Kyiv–Prague. As Chop is treated as the last stop on the Hungarian rail system there is at least one direct service to Budapest that originates here.
On services heading west from Kyiv and Lviv, domestic trains stop at Chop before reaching Uzhhorod; international services don't stop at Uzhhorod at all, as it is essentially at the end of a branch line from Chop. The quickest way between Chop and Uzhhorod is to take a marshrutka. It's also possible to catch buses from Uzhhorod to Hungary and Slovakia.