Here is an up-to-date list from NoCamels of 18 free activities in Jerusalem. Old City, Teddy Park, Knesset, Supreme Court, Wohl Rose Garden, Bird Observatory, Yad Vashem, Mount Herzl, Gazelle Valley, Montefiore Windmill, Skate park, Ein Karem, First Station, Sacher Park, Machane Yehuda and more.

https://www.israel21c.org/top-18-things-to-do-in-jerusalem-for-free/