The tourist information center at Nagano station can give you a bus and local train timetable to get to the monkey park, as well as a brochure with a handy map for the walk from the bus stop to the park. English spoken.
Yamanouchi town's Yudanaka Station is 45 minutes from Nagano on the Nagano-Dentetsu rail line; Nagano in turn is 95 minutes from Tokyo on the Asama bullet train. The train from Nagano to Yamanouchi is ¥1210 one way; then you need to catch a bus or walk.
You can take a public bus to Shiga Kogen and get off at Kanbayashi Onsen, which is an easy 30-minute walk away and costs ¥1300 one way. Alternatively - a minibus to the monkey park runs seven times a day from Yamanouchi town and costs 1,500 yen round trip, including admission to the park. WINTER ONLY.
Walking back down to Yudanaka Station from the park takes about 1.5 hours (possibly a bit longer in the reverse direction up). The route first follows the off-limit road along the river through forests before entering the beautiful spa town Shibu Onsen after that Yudanaka Onsen. A little further along the way stands a tall statue of a Kannon Buddha.
Jigokudani Monkey Park (地獄谷野猿公苑 Jigokudani Yaenkōen). Famous for its population of wild Japanese Macaques (Macaca fuscata), odds are you've already seen this place on TV. The best time for a visit is winter, when snow covers the ground and the monkeys come to bathe in the hot spring at the valley bottom — a unique sight. Many people come to this area stay in old traditional hot spring town Yudanaka-Shibu Onsen, experience stay in traditonal ryokan style accommodation, hot spring or skiing in Shiga Kogen - highest and largest ski area in Honshu island.¥500/250 adult/child. edit
Shimaya Hotel, Yudanak-Yamanouchi Town (at Yudanaka Station, go towards Lawsons then turn left up the hill. Shimaya is about 300m near a small grocery store). The building and interior are a bit old with Japanese style private and dormitory rooms. The owners are nice. Mr. Yumoto will drive you for free to Jigokudani Monkey Park or an amazing open air hotspring overlooking the valley or the local ski hill. Japanese and Western breakfast is available for a fee.¥3,500+. edit
Minshuku Korakukan Jigokudani, Jigokudani (Across the river from the monkey park entrance), ☎ 0269-33-4376 (fax: 0269-33-3244). checkin: 15:00. 10,000 yen to 14,000 yen. edit
Yudanaka Onsen Seifuso, Shin Yudanaka Onsen Yamanouchi-cho, Shimatakai-gun, Nagano-ken (Just past the little Shrine near Yudanaka Station. Shown on the map available at the station), ☎ 0269-33-3295 (fax: 0269-33-2811), . checkin: After 12; checkout: 10:00. Very limited English spoken by staff but they're friendly and will try to communicate with you. Drove me to the Monkey Park. Offer both Western and Japanese meal options; I'd recommend the Japanese option as the keiseki was fabulous. WiFi available in rooms10,000 yen to 14,000 yen. edit
Kokuya, Shibu Onsen, ☎ +81 26 933 251 (email@example.com), . checkin: 3PM; checkout: 10AM. Super-classy ryokan, run by the same family for 16 generations around 400years. 10 rooms with open air hot bath + 8 outside and inside hot baths. English spoken. 5min from Jigokudani Monkey park.Suites ¥16000-36900 (per person). edit