The Israelite Tower
This tower is not actually a museum, but rather it is an historical reminder set within modern Israeli society. Evidence of battles was found around the tower, and it was determined that this was the location of a specific battle on the 17th of Tammuz.
Currently, a school is located on top of the area, but tours are still available. To get to the museum a visitor must make an appointment and climb a large set of stairs. It is, however, an incredible view of an ancient battle through which the Jerusalem walls could not stand.
The Israelite Tower is located on Shonei Halakot Street, Jerusalem.
Source: Jewish Quarter Jerusalem