Do you need a vignette to reach Košice?
The Hungarian motorway vignette only covers the Hungarian section of your route. Once you cross into Slovakia, a completely different toll or vignette system takes over — OptimÚt calculates the Hungarian leg for you, up to the border.
Border crossing
Via Tornyosnémeti (M30): This cost/time covers the route to Tornyosnémeti (the Hungarian-Slovak border, M30 motorway) only — Košice is about another 20 km from there, where Slovak tolls/vignette apply.
How to calculate it
Open OptimÚt, enter your own starting point in "From", and type Košice into "To" — OptimÚt automatically recognises it as an international destination and calculates the route, toll cost and required vignette(s) up to the border, for whichever of the crossings above turns out faster or cheaper for your specific starting point.