Baradla cave is a must see of course.
I'd recommend the part from the Voros-to entrance.
But don't neglect the other caves there anyway.
There are not many restaurants in Josvafo. There's one decent in Tengerszem Hotel, and another one, kind of local eating place in the village centre, behind the drink bar. The food choice is not great, but you can eat there in a local, village athmosphere with friendly service. Of course one has to like that kind of places to enjoy it. For usual tourists, probably the Tengerszem will be a better choice. Or a restaurant in nearby Aggtelek.
Favorite Dish: I ate the Gipsy steak there. There are even some vegetarian dishes (usually cheese or mushroom dishes).