The imposing Castel Firmiano, dating back to AD 945, is the centrepiece of mountaineer Reinhold Messner's six museums. Based around humankind's relationship with the mountains across all cultures, the architecture itself suggests the experience of shifting altitudes, and requires visitors to traverse hundreds of stairs and mesh walkways. The collection is idiosyncratic, but when it works, it's heady stuff. Messner's other museums are scattered across the region, including his newest, at Kronplatz, and his most remote, at Ortles.
There's a shuttle from Piazza Walther in summer, or you can catch a taxi or take the suburban train to Ponte Adige/Sigmundskron (beware there is then a long walk up a truck-laden road). By bike it's a 25-minute ride along a riverside path.