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A museum dedicated to the life and legacy of Menachem Begin, the first member of an opposition party to be elected as Israeli Prime Minister.
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Gehenna
According to the Bible, this valley was once used for child sacrifice. Due to its association with evil, Gehinnom/Gehenna later became a name referring to Hell. Now, it is a pleasant though somewhat neglected park. If you come at night, you will see the cliffs lining the valley lit up in a variety of colored lights.
In 1948, Mount Zion was an isolated Jewish outpost exposed to Arab snipers on the Old City walls. A cable car was built between West Jerusalem and Mount Zion to safely provide supplies to Mount Zion. In this small museum, you can see the original cable car, as well as documents and other buildings relating to it. It was built as a hospital; now it is the Mount Zion Hotel, and the museum is inside the hotel.
Liberty Bell Park
The most visited park in Jerusalem, overlooking Mount Zion and the Old City. It features a replica of Philadelphia's Liberty Bell with the Biblical inscription - "Proclaim liberty throughout all the land unto all the inhabitants thereof".
Between 1948 and 1967, West Jerusalem and Mount Zion were under Israeli control, but the only access between them was vulnerable to Jordanian sniper fire from the Old City walls. To avoid this fire, a secret tunnel was dug so that Mount Zion could be safely supplied. Part of the tunnel was neglected and destroyed after 1967, but the remainder has been restored and you can walk up the mountain through it.
HaTachana HaRishona
Between 1892 and 1998, Jerusalem's train station was located here, not too far from the Old City. The station has since been reopened as an entertainment destination, with restaurants, shops, concerts, and more. There is something going on here every evening. A very nice linear park/bike path extends south from here all the way to Malha.
The first neighborhood of Jerusalem to be built outside the Old City. The Mishkenot Sha'ananim housing project and the landmark windmill were finished in 1860; the rest of the neighborhood was built in the 1890s. Nowadays the neighborhood is quaint, beautiful, surrounded by parkland, and with a direct view of the Old City walls. It's a delightful neighborhood to walk around, both during the day and at night.