Hi,
I am from Hungary, I can give you some hints. Anyway,
@MJB gave excellent advice, if that area fits you.
Some good places, just roughly:
I suppose you are interested in species that you are less likely to see in Britain.
1) Kiskunság National Park, near Apaj and Kunpeszér villages. Fishponds and flooded pastures where large flocks of geese and still some waders stop by. Good chance to see Red-breasted Goose, Lesser White-fronted Goose. Large open areas with steppe species, e.g. Saker, Bustard, Eastern Imperial Eagle.
2) Hortobágy National Park, near Hortobágy and Egyek villages: Large open grasslands with huge flocks of Crane and geese (incl. LWfG, RbG). Saker, Eastern Imperial Eagle are usual.
3) Tata, Öreg-tó (Old Lake): near the end of the month large flocks of geese, with LWfG and RbG, ducks and gulls. Woodpeckers (all resident species, except White-backed). There used to be a birding festival at the end of the month, see
Aktuális program | Tatai Vadlúd Sokadalom Really nice stuff, I used to be there as an organizer.
4) Börzsöny Mts.: White-backed Woodpecker is not too difficult to see, with some luck you can have even Ural Owl. They are most likely in the higher and inner parts. I live at this region.
5) Lake Balaton: by the end of Autumn, there used to be a variety of ducks, grebes, divers and gulls. At the area Kis-Balaton you can easily have Ferrugineous Duck. There are returning Greater Spotted Eagles wintering there.
If you specify what you are interested in, I can give more details.
Wherever you go, please, double-check the rules for visitors. In protected areas (Kiskunság, Hortobágy, Börzsöny) you may not be welcome if you leave the public road.
Attila