The second 'long distance' trip I took this summer was to Yudnaka and Matsumoto. To get here I took the train JR Chuo line from Nagoya to Nagano, transfering to a non-JR rail to get to Yudanaka and back to Nagano before traveling to Matsumoto and back to Nagoya using JR. You can also get to Nagano using the bullet train from Tokyo.
Once you get off the train in Yudanaka, this is the arch way that greats you to Yudanaka Onsen, but don't worry if you can't read it. The volunteers from the English conversation class of Yamanouchi Town has made information flyers for reference on how to get to everything. I got the impression that one of the volunteers was actually the mayor of Yamanouchi.
The monkey park is just outside of town, you can walk or take a taxi there from Yudanaka station. Walking takes about 1.5 hours, but it's a nice mountain trail.
When you see photos of the monkey park, you get the impression that it is really large. But in fact, it's really small, I was expecting a long hike to go from the ticket booth to the monkey hot spring area. But it was only about 10 minutes.
Don't mess with the monkeys.