The nearest major airport in Ukraine is Ivano-Frankivsk International Airport (IFO / UKLI). This airport has domestic flights from Ivano-Frankivsk, Ukraine and is about 180 km from UDJ.
The closest major airport to Uzhhorod International Airport is Košice International Airport (KSC / LZKZ). This airport is in Kosice, Slovakia and is 106 km from UDJ. If you're looking for international or domestic flights to KSC, check the airlines that fly to KSC.
Travelmath helps you find the closest airport to any city, as well as a list of smaller local airports. You can use these pages to plan your trip and figure out the easiest way to get to your destination. Many times there are multiple airports near the city you want to visit, so you can often find a cheaper flight into a different airport. This is especially useful if you are getting a rental car, since it might be better to drive a bit farther in order to save money on airfare. If you're booking an international flight, you probably want the closest major airport, otherwise if you're a pilot you may be looking for a local airport. Use this tool along with the flight distance pages to plan your travel.