Taking the Japanese rail

Hello!

So I've been researching the Japanese rail for when my boyfriend and I are planning to go out to Japan in October. From October 20th to November 4th, we plan on buying the JR rail pass for when we stay in Tokyo. What I am at a loss at is what we should get for when we go out to Kyoto and Osaka for 3-4 days. For the rail pass for out in Kyoto and Osaka, I know there is a JR pass to use out there but is that unlimited use for a specific period of time? If not then what would you recommend?

Also if anyone has some recommendations for a good Hot springs place to stay? We want to have our own private room and private bath for the two of us to use. I also have tattoos so anything tattoo friendly in Osaka and Kyoto would be preferable.