The JR Pass is not as useful as the Suica for transportation in the Tokyo-Yokohama area (it doesn't cover the subway, for example), but it is very useful for intercity travel.

There is a "back way" to Kyoto on the Chuo Line via Shiojiri to Nagoya and then around the top of Lake Biwa to Kyoto, so if the Shinkansens are all booked up, that may be an alternative. (See a railroad map if you can't visualize what I'm talking about.)

Book your trains the day you arrive, and then you'll know whether you can get reserved seats or not.

One of the other great things about Japan is that there are usually several ways to travel between any two points.