There is a very muraculous icon and a monastery in Mariapocz, which is a place of pilgrimage for both Greek Catholics and Orthodox.
http://www.viragos.info.hu/t1998/mariapoc/e_tel.html I found this adress where you can find information about the GGC in Hungary and the adresses of the parishes, but i don't know if it works:
szaplonc@mail.tiszanet.hu
You can also reach the Eparchy through its adress. It has its see in Nyiregyhaza:
Hajdudorogi Puspoki Hivatal, Pf. 60, Bethlen Gabor u. 5, H-4400 Nyiregyhaza, Magyarorszag
Telephone: (42)415-901
Fax: 415-911