I remember visiting an Onsen Town that was famous for making Kokeshi (Japanese Wood dolls).
I found it in my webblog,
klick here to see some pictures.
The place is called Naruko Onsen and is north of Sendai. Its not so close to Tokyo but with the Shinkansen you can be in Sendai really fast and if you spent a day in Senday seeing
Matsushima as well it might be worth a trip.
For a nice relaxed Onsentown (even Naruko Onsen off course has lots of Onsen) i would recommend
Akiu Onsen wich you can reach in less than 1 hour once you are in Sendai. Akiu Onsen is really out of the way and not so touristy as most places. I´m sure you can find a hotel there that offers a private bath or a mixed public bath.
You can also check for Ryokans in Naruko Onsen wich feature a private bath or a mixed one if you don´t have time to spent 1 day each.
I definetly recommend Matsushima bay if you can make it. I´ve travelled most of Japan and this was one of my Top 3 places and it is considered one of the Top 3 offilialy as well. Naruko Onsen was nice as well and would eventually be interesting for wood making (even its no furniture).