Prepare for unexpected vet bills
Hungary has a number of beautiful beaches that are open to the public, as well as a number of beach resorts that each have varying prices. The previously mentioned Lake Balaton, for example, has gorgeous beach nearby in addition to the fabulous hiking trails. The town of Siófok is also another great area to have some fun in the sun.
Hungary has a number of well known cities and landmarks that have become world famous over the years. Why confine yourself to only seeing one of them when you could go on a tour with your dog across the "Heart of Europe?" There are a number of tours, spanning multiple days, that will take you and your dog through the likes of Prague, Vienna, and Budapest.