On the suggestion of the owner of Sandal Wood, I visited Tenryuji, which is maybe a 20 minute bicycle ride from Ninnaji. It has a very country feel; you bike past a bunch of rice paddies.
Tenryuji has a famous zen garden, which is very worth visiting. I took an extra long time touring, because after walking and biking around all day with 20 pounds on my back, I was really tired and had to sit down a lot. Tenryuji was not originally on my list, but I am glad I took the owner’s advice to visit it, and I highly recommend the garden.