Ten or fifteen minutes' walk east of Matsumoto station, Fukashi-jinja is a large Shinto shrine, dedicated to two local deities: Suwa-myojin, the god of war, and Sugawara-no-michizane, the god of learning.
There are plenty of attractive or interesting things to see here. By the main gate, there's a small shelter over a trough for purifying your hands with water, and under the eaves there are brightly colourful painted carvings. Then as you progress into the shrine grounds, there are some impressive statues of guardian lions, and one of a resting bull.
The main prayer hall is also ornate and painted in bright colours, and nearby there's another statue, standing by a very small but charming patch of flowers. This one is of a scholar, and looks like it's gold-plated, but presumably isn't.
Whlie you're here, it's definitely also worth visiting neighbouring Zenkyu-in, an atmospheric Buddhist temple populated by a wide range of interesting statues.
From Matsumoto station, head east along Agata-no-mori street, then turn south at the Miyamura-machi traffic signal, just before the Performing Arts Centre. The shrine is a couple of minutes' walk from the signal.