One of the more famous places in Kyoto is called Ginkakuji (not to be confused with Kinkakuji). They’re actually quite far apart, and the style is quite different. Unlike Kinkakuji, which is a reconstruction, Ginkakuji is the original temple from the 15th century. It has some gardens as well and isn’t nearly as crowded, so it’s actually fairly nice to visit.
The easiest way to reach Ginkakuji is by bus; it can be reached by number 102 or 203 buses from Demachiyanagi (Keihan line) and by number 17 or 5 buses from either JR Kyoto station or Shijo Kawaramachi station (Hankyu).
Ginkakuji is open from 8:30 to 5:00 from March 1st to November 30th and from 9:00 to 4:30 outside of then. Adults are 500 yen and children under 13 are 300 yen.