Most of travellers who stay in Tokyo think about visiting Hakone (箱根). It is only a few hours away from Tokyo. It is well known as one of the most popular hot springs resort in Japan. And also it is very close to the highest mountain in Japan, Mt. Fuji. But Hakone is not connected with Tokyo by Japan Railway. That means Japan Rail Pass cover limited part of your trip to Hakone. Odakyu Electric Railway (小田急電鉄) that is one of the major private railway companies in Tokyo and Highway bus are more convenient way to get there. Though Japan Rail Pass cover limited part of travel, some of you still think about using Japan Rail Pass as much as you can and try to minimize the extra cost.
As you know, Mt. Fuji is the highest mountain in Japan. Sometimes we can see it even from downtown Tokyo. And when you travel to west from Tokyo by Shinkansen, you will be able to see this beautiful shaped mountain through the window on your right side.
*If you want to see Mt. Fuji on Shinkansen, when you reserve the ticket for Tokaido Shinkansen, try to get D which is isle side, or E which is window side unless you travel as party of 3. The seat configuration on Shinkansen is 3 (A,B,C) + 2 (D,E). (If you take Green seat, C and D are the right place to see it.) Even if you travel to opposite direction (from Osaka to Tokyo), the seat configuration is same. D and E are always on the mountain side.