If you have time to check out only one restaurant in Hungary, then make that Napfényes! This is a place where you could taste all the traditional Hungarian dishes in a vegan version. They even have all the cakes that bring back the flavors of my childhood. If you prefer a pizza with vegan cheese, this is a place for you too: there is an amazing selection of toppings to choose from.
Their newer restaurant is bigger. It is at 1053 Budapest, Ferenciek tere 2.