If you’re looking for a day trip just outside Tokyo, Kamakura is the place to be. Kamakura is one of my favorite cities and has many historical temples and shrines. Komachi Dori, the main shopping street located in front of Kamakura station, offers all kind of traditional foods and sweets. The Tsurugaoka Hachimangu Shrine, the most important Shrine in Kamakura can be find at the end of Komachi Dori. Tsurugaoka Hachimangu Shrine is open from 5:00 – 21:00 (6:00 – 21:00 from October to March). Free entry. Official website (in English): http://www.tsurugaoka-hachimangu.jp/
Another recommended spot is the Great Buddha of Kamakura, also known as Daibutsu. The huge, bronze Buddha was cast in 1252. You can enter the Buddah as well for only 20 yen. Daibutsu is part of Kotokuin Temple and is daily opened from 8:00 – 17:30 (17:00 from October to March). Entry is 200 yen. Official website (in English): http://www.kotoku-in.jp/en/top.html
You can easily spend more days in Kamakura as the historical city has much to offer.