Hi JJ,
I took some extra time to think about this one, as 15 days is a good amount of time to travel around in Japan, so you've got a wide range of potential places to visit.
Since you arrive late afternoon on a Sunday 16:00, I would head into Tokyo for at least one night to relax from your long distance flight and indulge yourself a little with some Japanese cuisine. The next day you could either stay an extra day in Tokyo or start your train travel throughout Japan.
Going to your Itinerary, I would head to Takayama first and stay 2-3 days here and explore the area. The train ride is one of the most scenic in Japan, first you take the Shinkansen from Tokyo station to Nagoya, on a clear day you will have a beautiful view on the right side of the train of Fuji-san. Once at Nagoya station, you will transfer to the Wide view limited express headed to Takayama, the train will follow a riverbed running trough mountainous area and the various mountain views are just stunning.
After Takayama you have a couple of options, a popular and next destination is Kanazawa, which is also located on the upper side of Japan and is great next stop. I would recommend staying here for 2 nights to explore the city and neighboring area.
After Kanazawa you can take a direct limited express train (called the Thunderbird) to Kyoto, where you can explore Kyoto and the Kansai Area (such as Osaka, Nara and Kobe). From here I still think that you have enough time for a next destination and I would hearty recommend a visit to Hiroshima. In Hiroshima you can visit the peace museum and memorial park. I've always felt that this is one area in Japan that leaves a deep impression because part historical events. You can also make a visit to Miyajima Island from Hiroshima, which is also covered by the JR Pass.
After Hiroshima it is time to head back to Tokyo but you could make an other nights stop along the way, at Osaka, Kobe (if you haven't visited them yet) or perhaps Nagoya. You may still have a couple of days left in Tokyo depending on how long you stayed in each other place. You can use these for to explore the city more, do some shopping and maybe even a day trip to Nikko.
Travel time from Kyoto to Narita Airport takes about 4 hours by train so I would not travel there on the same day if you have an outgoing flight at 11.00 a.m.
You would be making really good use of your JR Pass with the above itinerary!
I hope this helps!
Daniel
