Here are a few sites that your might or might not have visited, about trains and passes:
http://www.ttasfo.com/pages/tokyu_jr.html
http://www.japan-guide.com/e/e2017.html
The Yamamote Line is a JR operated train in Tokyo. It circles the city, and connects to many subway lines.
I also concur that 3 days in Kyoto would be enough, so that you have equal time in Tokto.