Get a japanese rail pass which allows you to use all forms of rail transport.
http://www.japanrailpass.net/eng/en001.html
There are some private lines which aren't included, but on the main routes, its valid. I think it explains it all onthe website
Plenty of awesome Shrines (the golden pavilion/Kinkakuji to name one) in Kyoto as well. I'm going for 2 weeks in August/September to see family, I can't wait. Its been ages since I've been. Also, going up to the top of Kyoto train station, you get a cracking view across the city, obviously not as good as from the tower, but still, its free.