Bükfürdő sits in an unusually rich corner of western Hungary for day excursions. The medieval walled town of Kőszeg is 20 km to the south — its Old Town is one of the best-preserved in Hungary, with baroque architecture and a famous fortress where a handful of Hungarian knights held off the Ottoman army in 1532. Sopron, 46 km north and reached in under an hour, has the largest concentration of historic buildings in Hungary outside Budapest, plus good wine from the Fertőmelléki wine region.
Nagycenk, 35 km north, has the baroque Széchenyi family palace and the charming Nagycenk Museum Railway — a narrow-gauge line running through the estate, operated partly by children. It pairs naturally with a visit to the nearby Fertőd Palace (Esterházy Palace), arguably Hungary's most impressive baroque country seat, where Haydn spent most of his career.