After lunch, hop on the E60 toward the small town of Rorschach, on Lake Constance; just beyond Rorschach is a wooden bathhouse where you can stop for a restorative dip. In the afternoon, cross into Austria and turn onto Route 13 toward Bregenz, a lakeside town with contemporary art museum Kunsthaus Bregenz (Karl-Tizian-Platz, Bregenz; 43-5574/485-940). The glass-and-steel building, designed by renowned Swiss architect Peter Zumthor, showcases rotating exhibits—this year the focus is on artists from Asia. It’s just 23 miles southeast on the B200 to the Alpine town of Bezau. Check in to the 54-room Hotel Post (35 Brugg, Bezau; 43-5514/22070; hotelpostbezau.com; doubles from $320, including breakfast and dinner), where the fifth-generation owner Susanne Kaufmann has infused just the right amount of modern flair into this classic country inn: staff are decked out in traditional Austrian garb (dirndls) and rooms are appointed with blond-wood tables and white leather sofas. It helps that Kaufmann’s brother, superstar architect Oskar Leo Kaufmann, oversees the design. For dinner, there’s local favorite Engel (29 Platz, Bezau; 43-5514/2203; dinner for two $122), which specializes in hearty Austrian classics including cured pork belly and potato salad.