There is also much to see outside the Old City including the bustling downtown districts of East and West Jerusalem ; the ancient sites and vistas on the Mount of Olives and in the Kidron Valley ; and , on the western hills of the city , the dynamic Israel Museum , the powerful Yad Vashem Holocaust Memorial and Museum , and the contemporary buildings that house the Knesset and the Supreme Court of the State of Israel .
There is much to see outside and inside the Old City .