It depends on what time of the year you're going, but I enjoyed traveling to Yoshino, south of Kyoto, on a recent trip. It's a famous cherry blossom viewing and autumn leaf viewing site, at which times it is said to be completely overcrowded. I went before the best leaf viewing time, and I found it pleasant, restful, friendly, and a good glimpse of rural Japan.

You can go all the way there on the train (private railway), with the last stop being a funicular to the top of the mountain where the village of Yoshino is.

Another reason not to rent a car is that the Japanese drive on the left. This may not be a problem for you if you come from a country where that is the case, but if you're from North America, it will add a bit of confusion on top of your expenses.