The fastest transport to Košice is, of course, by plane: https://www.airportkosice.sk/en/node/310
From the airport you can get to the city center by bus (number 23) or Bolt Taxi.
Trains and buses run regularly to Košice. We recommend contacting the local train or bus station to find out how you could be transported to Košice.

Kosice is a beautiful city that you should definitely visit!