Jerusalem abounds in cultural options. There is a large number – and wide range – of museums, an untold number of cafés, bars and restaurants, and lots of music, as well as regular lectures on a host of topics. While in some ways the city is undergoing a process of what could be regarded as "orthodoxization,” parallel to this, secular activities are burgeoning, ensuring that locals and tourists have what to do and where to go at any time, even on the Sabbath and religious holidays.
During Saturday, the Old City (except the Jewish Quarter) is full of life. The Jerusalem Cinémathèque is also open, as well as their restaurant/café (http://www.jer-cin.org.il/Default.aspx?Lang=En). Films not in English, including Israeli films, usually have English subtitles. The Old Train Station, as well as the Biblical Zoo, is also open.
Some people would argue that there is a disproportionate number of museums in Jerusalem, considering its small size. An excellent site with descriptions and details of many of Jerusalem’s museums is www.ilmuseums.com. Check it for current opening times, entrance fees, etc. The Israel Museum (http://www.imj.org.il/en/), among others, is open on Saturday.