You can get two really good day trips out of Matsumoto: one for Matsumoto Castle and the inner city in general, and one for Kamikochi (https://www.kamikochi.org/). It's also easy to go from there to Kofun or Nagano.
For other advice I would recommend that at least one of your group speaks enough Japanese to ask directions, order food, use a laundromat, shop at a supermarket, describe what you want at a barber's, tell a doctor what you're ailing, ask a staff member where the lost and found is, that kind of stuff. Also note that New Year's and Golden Week are really awkward times to go and summer is hot and humid. Make sure to talk to your GP to make sure you have whatever vaccinations you need, I'm thinking of Japanese Encephalitis (JE) in particular. Also make sure you take enough cash to get the most basic necessities if the airline manages to bungle your luggage. In short, just keep all the basic travel advice in mind and you'll be fine.
For other advice I would recommend that at least one of your group speaks enough Japanese to ask directions, order food, use a laundromat, shop at a supermarket, describe what you want at a barber's, tell a doctor what you're ailing, ask a staff member where the lost and found is, that kind of stuff. Also note that New Year's and Golden Week are really awkward times to go and summer is hot and humid. Make sure to talk to your GP to make sure you have whatever vaccinations you need, I'm thinking of Japanese Encephalitis (JE) in particular. Also make sure you take enough cash to get the most basic necessities if the airline manages to bungle your luggage. In short, just keep all the basic travel advice in mind and you'll be fine.