European Summit Challenge
Most people arriving in Hungary from the west will do so via Budapest, Hungary's capital city. Take the train from Budapest's Keleti pu station to Vamosgyörk (~1 hr 15 mins) and then on to Gyöngyös (another 15 mins). Gyöngyös is a large town and makes an ideal base. Alternatively continue on to Mátrafüred via the private narrow gauge railway.
You can start walking from Gyöngyös though there is little height gained until one reaches Mátrafüred. From Mátrafüred, the route to the summit of Kékes is entirely forested, and paths are waymarked using an array of colour coded shapes. The most direct route to the summit is waymarked by blue cross, later by blue triangles. I took an alternative but parallel route down following green blazes. At no time did the route present any difficulties.
The easiest, but perhaps the most boring route would be to follow the road to the radio mast on the summit.
Accommodation can be found in both Gyöngyös and Mátrafüred. In Gyöngyös I stayed at the guesthouse Vincellér Panzió at 22 Erzsébet Királynét. I found both clean and reasonably priced.
The Hungarian Tourist Board Website has useful fact about travelling to Hungary.