There are a disproportionate number of dental offices in western Hungary because Austrians frequently cross the border for cheap, high-quality tooth care. About 15 minutes from a border post that is about as relevant today as it was at the height of the Habsburgs, you can tour “the Hungarian Versailles,” the ancestral home of the Eszterhazys, arguably the most powerful family of the old empire. In the late 18th century, Joseph Haydn was a composer in residence for several decades. More recently, Soviet troops sacked the place on their implacable march into the heart of the Third Reich. The palace, now a walkable museum, has several old wooden doors crudely stenciled with hammers and sickles.