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Archaeological digs have shown that this hill is the Biblical city of Gibeah, which was King Saul's capital before David came to the throne. The ancient ruins are not visible, but you can see a large ruined modern building. King Hussein of Jordan started building a palace here in the 1960s, but the 1967 war interrupted this and the palace was never finished. Be careful around the palace ruins, as they are not in good repair. There is a good view from here of the surroundings.
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Givat HaTachmoshet
This was the main Jordanian fortification in East Jerusalem. Israel overran it in a bloody battle in 1967, leading to the capture of all of Jerusalem. Now the Israel Defense Force runs a museum here commemorating the battle.
An ancient underground tomb with 23 niches, matching the 23 members of the "Minor Sanhedrin" (an ancient Jewish court).
Kever Shimon HaTzadik
An ancient cave tomb, traditionally the burial site of Simeon the Just, a Jewish leader and high priest in the 3rd or 4th century BCE. If you cannot get to Meron for the annual Lag BaOmer festivities, there is also a celebration here.
The humanities faculties of Hebrew University, Israel's top-ranked university, are located here. The campus is quiet and leafy, but confusing to navigate. There are impressive lookouts on the Old City to the south west and the Judaean Desert to the east.