Matsumoto city is an excellent and compact city with lots of local soba restaurants, izakayas, and some tourist attractions. You can ride a bike for free if you sign up at the bike parking in front of the railway station. If you plan to stay for more than one day, you can also go to some lovely places in the surroundings, soak in warm onsen water, hike through forest tracks or visit some spiritual places.
Matsumoto Castle is undeniably an icon of the city that lures countless tourists who are staying in Nagano prefecture to visit Matsumoto. It is a 6-story building and is for many surprisingly small, as it appears quite big on pictures. Nevertheless, the castle’s interior is a treasure box containing several artifacts, mostly guns, and might be more interesting than the visit of Osaka castle. You can also get to learn more from very friendly Japanese volunteers who speak English. The castle is enlightened during night-time and is a picturesque object for photographers both day and night.
Former Kaichi School is one of the first schools in Japan located near the Matsumoto castle. The building is a unique combination of western-style and Japanese architectural elements. In 1961, it was designated an Important Cultural Property and the museum offers an interesting insight into the education of Edo period.
Strolling through the center is enjoyable. If you head south after visiting the castle, you will cross two nice street along the Ta river. Nawate street is ostensibly devoted to frogs and you can surely find many of them on this narrow pedestrian road. Apart from Yohashira Shrine, you can also find here many small shops with souvenirs, food and more. If you cross the river, you’ll find yourself on Nakamachi street, a bit more modern shopping street with also some café’s and beer brewery.
My recommendation is to also visit Matsumoto City Museum of Art. When I was in Matsumoto, there was an exhibition Kusama Yayoi, a native of Matsumoto, and façade, as well as statues in front of the museum’s building were paying homage to her polka dot pop-art works. To check for current exhibitions, go to: http://matsumoto-artmuse.jp/exhibition/.
In order to have a nice view on the city and Japanese Alps in the background, you can go to Joyama Park which is not that far from the city center. There’s a small tower which you can climb and enjoy the view.
You can also indulge in hot springs nearby, namely Asama, Tobira, or the milk-white water of Shirahone. In case you have a car, I also suggest visiting Gofuku-ji Temple, a spiritual place hidden in the mountains near Matsumoto city. Another great tip for a trip outside of the city is to visit Kamikochi where you can enjoy pristine nature of highland valley.