*Not* any JR train - you can't use the fastest bullet trains (Nozomi or Mizuho) for example. But you could with the regional passes that also involve bullet train routes. Also on the JR pass there is a small number of train lines, mostly formerly run by JR, where you'd have to pay extra. You can get more info on: http://www.japanrailpass.net/en/about_jrp.html
Otherwise you can ride JR lines all over the country.
The JR Pass is meant to produce savings for longer distance travel between cities. Any JR lines that you happen to find convenient to use within a city is just a plus.
You can use the JR Pass within Kyoto to go from Kyoto Station to Arashiyama, as well as down to Uji (and farther along, Nara). The same line also allows you to go to Tofukuji Shrine and Fushimi Inari Shrine. As said though, the JR pass is made for long distance travel.
Comments
http://www.japanrailpass.net/en/about_jrp.html
Otherwise you can ride JR lines all over the country.
I would say that's pretty fair!
The JR Pass is meant to produce savings for longer distance travel between cities. Any JR lines that you happen to find convenient to use within a city is just a plus.
Again, please don't piggyback your questions.