Temples are for Buddhism, whereas Shintō shrines honor Shintō deity. Japanese people often say that you can make a wish at a shrine but not at a temple. Actually, strictly speaking, it depends on the temple’s denomination. For example, temples of the Jodo‐shin and Zen Buddhist sects are not places where you go to make a wish, but there are many other Buddhist sects where making a wish is fine. In fact, many esoteric Buddhist temples will offer up special prayer ceremonies for you just as Shinto shrines do. The most popular shrines and temples for hatsumōde (please click here for details) in the Tokyo area are 1. the Meiji Shrine, 2. the Narita-san Temple, and 3. the Kawasaki-Daishi Temple.
