If you take the JR line to Harajuku, the Meiji Shrine is just to the west of the station. The large, leafy park is a welcome respite from the hustle and bustle of Harajuku.
The Meiji Shrine is dedicated to the emperor Meiji and his consort, Shoken. Meiji died in the early part of the 20th century. There are tens of thousands of trees here.
Meiji Shrine is located near the center of the park. The entrance is free. If you'd like to offer your wishes then go up to the shrine, throw a coin in the box and bow your head, clap your hands, wish for something, clap your hands again and bow. There are charms and other things for sale in little booths to the east.
The rest of the park is much less crowded then the central shrine area and is a great place for a walk. There is 'Treasure Museum' to the north but the offerings are quite slim (many recent portraits of emperors and empresses and a carriage). There is also a museum annex in the southeast area of the park, next to the big gift shop and restaurant. This annex presents rotating exhibits, some quite good. Entrance for the 'Treasure Museum', which includes the annex, is 600 yen but students get a discount.
The official website in English can be found here: www.meijijingu.or.jp/english/index.htm