Once upon a time I went to Hungary and was amazed and questioned why they say Hungary has the most alcoholics; well it became apparent when I realized everyone I visited had their own wine cellars and breweries.
In America the popular choice of Hungarian wine is Egri Bikavér, or an occasional bottle of Tokaji wine.
Egri Bikavér is a red wine - you can pick from a sweeter or tarter version in most wine stores - this is not a typical wine from my experience that can be purchased in your local supermarket.
Egri Bikavér is made of several grapes including the: Kadarka, Kékfrankos, Kékoportó, the Cabernets, and Medoc Noir. Unfortunately prior to 1990 before the communist era ended in Hungary the Kadarka grape was eliminated from the recipe due to it's being hard to cultivate and grow. Since the 1990s Hungarians have put back the kadarka grape back into the recipe to re-gain it's exquisite bold wine color and flavor.
The cities of Szeged and Eger are the manufactures of this wine. Szeged in the south-eastern part of the country and Eger is in the north-eastern, when looking at a map they are almost directly in line with one another. Eger is not nor was in Transylvania.
My grandmother also noted in her book that this is a good medicine for stomach problems and helped against ulcers and such.
And of course like any good wine it's best served aged and chilled.
determined exact location of cities: http://www.gotohungary.com/budapest/hungarymap.shtml
All information from grandma's recipe book and reprinted with permission.