Start in the hub town of Matsumoto, where you'll visit the famous black-walled castle, one of only twelve original castles remaining in the country. From here you can visit the nearby Jigokudani Park, famed for its iconic snow monkeys (if travelling between December-April). Watching the Japanese macaques soak in the natural hot springs is a bucket list Japan experience and makes for some extremely adorable photo opportunities. If you're travelling during summer, rather than monkey spotting we would suggest you walk the well-marked Kamikochi nature trails in the valley to the west of Matsumoto, where you'll follow the bright blue waters of the Azusa-gawa River through the lush mountain terrain.
Traditional Takayama is another of the Japanese Alps towns well worth a visit. Here you'll find a beautifully preserved shitamachi (old town) and can stay in a ryokan (traditional inn) for the real authentic Japanese experience. The walking here is also great and includes the two-mile Higashiyama Trail, which you can celebrate completing with a drink in one of the many sake breweries back in town.
As a final stop on a tour of the region, include the UNESCO World Heritage Site of Shirakawago, which can be visited on a day trip from Takayama. A small village in the mountains, Shirakawago is known for the distinctive thatched roofs of its farmhouses and is a great place to really feel like you're exploring rural Japan.
