In the morning Nakanoyu runs two shuttle buses to Kamikochi at 8am & 9am.
Then there's the bus back to Matsumoto from Kamikochi bus terminal at 12:30 I think?
So in theory you can have about 4 hours in Kamikochi and back to Matsumoto with zero transport costs!
I have however booked 2 nights in Kamikochi, so took the 9am bus and got off at Taisho Ike (Ike = Pond).
Kamikochi 上高地, if you want to know more...
Chubu Sangaku National Park
www.kamikochi.org
In short, Kamikochi is a 15km long valley along the Azusa River, about 1500m above sea level. Surrounded by mountains such as Nishi Hotaka Dake, Oku Hotaka Dake(3190M), Mae Hotaka Dake, Yake Dake, Myojin Dake...etc. These are all part of Chubu Sangaku National Park.
A map is necessary!
Otherwise you won't know what I'm talking about for the next few chapters
At the Southern end, Nakanoyu onsen is already in the Kamikochi restricted area (private cars are banned). If travel by car you can only reach either Hirayu or Sawando car park, from there take the bus or taxi to Kamikochi.
Bus terminal near Kappa Bashi is where most day trippers get off. You can start from Taisho Ike and hike all the way to Myojin Ike and back, I think that would be the limit for a day trip.
Beyond Myojin Ike, it's turing into more of a hiker/climber world. From Yokoo upwards there's proper mountain excursions to be done.