Košice is the largest city in eastern Slovakia. It is situated on the river Hornád at the eastern reaches of the Slovak Ore Mountains, near th…Košice is the largest city in eastern Slovakia. It is situated on the river Hornád at the eastern reaches of the Slovak Ore Mountains, near the border with Hungary. With a population of approximately 230,000, Košice is the second-largest city in Slovakia, after the capital Bratislava.