Slanec Castle is a hilltop ruin southeast of Kosice, with roots in the 13th century. It was abandoned after the 17th century, partly revived as a family museum in the 19th, and left in ruins again after the Second World War.
The surviving tower and walls are the draw, along with the walk up and the views over the surrounding countryside. It is a good half-day target if you have already seen central Kosice.