It's a fair way from the centre of Matsumoto, maybe thirty or forty minutes' walk from the station, but if you're in that part of town, possibly after visiting the castle or the nearby excellent French restaurant Bistro Kotsuna Seta, Taiangaku-ji is definitely worth stopping by.
More than most Buddhist temples, it's a very striking mix of old and new. The prayer hall is clearly recent, with the fine detail still pristine on its beautiful wooden carvings of birds, dragons, demons, an airborne deity; above the fiercest dragon, there are painted panels on the ceiling, lush flowers in bright colours.
On the other hand, there are also some much older features: the gate is home to two centuries-old statues of menacing guardian demons, there's a statue of a Buddhist pilgrim standing stoically in the grounds, and possibly also in the gate (I forget exactly where: forgive me) there's a very old, battered Buddhist deity mounted on horseback, the wood discoloured and weathered with age.
The temple is close to Okanomiya Shrine, around ten or fifteen minutes' walk north-east from Matsumoto Castle, or a few minutes directly east of Bistro Kotsuna Seta.