Matsuyama has one of the oldest and most famous onsens in all of Japan: Dogo Onsen. I went there and it was great! Be sure to take your own bath towel from the hotel, they only rented hand towels there, which are not nearly enough to dry yourself with.
DOGO ONSEN
Matsuyama Travel: Dogo Onsen
Dōgo Onsen - Wikipedia, the free encyclopedia