The Koniar plateau is a slab of limestone lifted above the surrounding valleys in southern Slovakia, one of the high karst tablelands that together make up the Slovak Karst. From the road it looks like nothing much: open grassland, scattered trees, a few pastures, steep wooded edges falling to the valleys of the Slaná and its tributaries. The interest is underneath. Rain soaks straight through the limestone, carving caves, shafts and swallow holes, and the whole cave system of the Slovak Karst and Hungary's Aggtelek, just over the border, is protected as a single World Heritage site. Nearby you will find the Ochtinská aragonite cave, filled with white needle-like crystals, the Gombasecká cave with its thin straw stalactites and, further north, the Dobšinská ice cave.
Up on the plateau the vegetation is unusual for Slovakia, with steppe grasses, orchids and warmth-loving shrubs on the dry, thin soil, and in early summer the meadows are full of butterflies. Raptors circle over the edges. The views from the rim are long and wide, over gentle hills and villages with red roofs and church spires, and in autumn the beech woods on the slopes turn bronze.
The riding around Rožňava, Plešivec and Štítnik is relaxed and pleasant. Roads are mostly quiet two-lane routes threading along valleys and over low ridges, with a few properly entertaining climbs where the road leaves the valley floor and switchbacks up through forest. Surfaces vary, from fresh asphalt to patched and broken tarmac in the villages, and you will meet horse carts and slow farm traffic in places. North of here the roads into the Slovak Paradise and the Low Tatras become steeper and more alpine in character.
This area is rich in castles and manors. Krásna Hôrka, above the village of the same name near Rožňava, was gutted by a fire in 2012 and has been under restoration since, and the Andrássy manor at Betliar, with its big English park, is a lovely place to walk. Rožňava itself grew rich on mining and has a handsome square. It and Revúca are the towns for fuel, food and lodging; Dobšiná is smaller but useful too. On the plateau itself there are no services at all, so bring water.