The Kamakura Daibutsu Trail Starts Beside a Temple, Not Inside It
This trail is free, and the reason is geography. The entrance is not the gate of Jochi-ji. It is a flight of mossy steps past it, with no gate and no window.
Kamakura
Hiking trails in Kamakura: the free Daibutsu trail, the Ten-en ridge, and which end you start from.
Kamakura Tenen Trail: What the 500 Yen at Kencho-ji Actually Buys
The trail is free. The way onto it is not. From Kita-Kamakura the Ten-en ridge starts at the back of Kencho-ji, and 500 yen buys the 22 minutes before it.
Kamakura Hiking Trails: Which End You Start From Decides What You Pay
Both trails are signposted in English, and so is the price. One starts inside a temple that wants 500 yen in cash, and the end you enter from decides it.