This itinerary can be comfortably completed in a week to ten days.
Planning your train route: Japanese Train Route Finder By Jorudan Co.,Ltd. You can save money by buying a rail pass before you go to Japan. Although the passes cannot be used on the very fastest trains, the “Nozomi” and “Mizhuho”, they are good on the other high-speed Shinkansen trains.
Hotel Sunroute Plaza Shinjuku -modern Western-style hotel, very inexpensive (get a double for less than $150 a night), next to a major rail station and the amazing Isetan department store. Be sure to vist the high-end food stores in the lowest level of the Isetan.
Ghibli Museum - a wonderful homage to animation. It is quite small, but plan to spend most of a day to experience it in full. You must purchase tickets far in advance. In the US, you order tickets from the JTB travel agency. It is about a 20 minute train ride from Shinjuku station to Mitaka station, and then another 20 minute walk from the station to the museum.
Nara - Japan's ancient capital, a short train ride from Tokyo. Wander the Deer Park and tour Todiaji Temple.
Ryokan Shimizu: the inn with the true feeling of Kyoto - inexpensive and foreigner-friendly.
There are thousands of historic sites Kyoto. On your first visit, be sure to take in Kiyomizu-dera Temple, Nijo-jo Castle, and Ryoanji Temple. You can spend any number of days in Kyoto and not begin to exhaust its treasures. Finally, take the train through the mountains to...
Wander Takayama's delightful streets of historic shops. Stay at least one night.
Plan to spend one or two nights in this ancient mountain village, staying and taking your breakfast and evening meal in a traditional gassho-zukuri style farmhouse. You will need to take a bus from Takayama to Shrakawa-go - note that there are only a few buses a day, so check the schedule in advance.
Japanese Guest Houses: Ryokan Styles - where you can reserve a traditional guest house. This web site also lists guest houses in dozens of other historic villages and cities across Japan.
Finally, take the return bus to Takayama and the train back to Tokyo.