Not to Mt. Fuji. For there, you'd need to choose between going to Hakone or the Fuji 5 Lakes area. JR can't take you all the way to either. There are good Odakyu passes for those areas though. http://www.odakyu.jp/english/deels/
While going down to Kyoto, you really should give a half or full day for Nara as well. It has some of Japan's best sights. The JR Pass is of limited use in Kyoto - you can use it to go see Arashiyama on the city's west side as well down the Nara line to see the Fushimi Inari Shrine, Uji, and Nara. Otherwise there is a good 500 yen bus day pass that can help you. When you arrive at Kyoto Stn, a visit to the tourist info office on the 2nd floor is worthwhile too - you can get good info, maps, etc.
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There are good Odakyu passes for those areas though.
http://www.odakyu.jp/english/deels/
While going down to Kyoto, you really should give a half or full day for Nara as well. It has some of Japan's best sights. The JR Pass is of limited use in Kyoto - you can use it to go see Arashiyama on the city's west side as well down the Nara line to see the Fushimi Inari Shrine, Uji, and Nara. Otherwise there is a good 500 yen bus day pass that can help you. When you arrive at Kyoto Stn, a visit to the tourist info office on the 2nd floor is worthwhile too - you can get good info, maps, etc.