On a clear day, you might be able to see the Dead Sea. Maybe.
Rising out of Jerusalem's northeast corner, offering commanding views of the entirety of the Old City and much of West Jerusalem beyond, is Mount Scopus (Har Ha'Tzofim), one of the seven hills upon which Jerusalem is supposedly built, a relatively modest mountain that still figures prominently in the city's history and continues to capture the Israeli imagination.
The mountain is so-named because it served as the lookout point from which Roman troops planned their assault on the rebel-dominated city of Jerusalem during the Great Revolt of Judean revolutionaries in the 1st century CE. The Hebrew University, the first secular Hebrew language institution of higher learning ever established, was opened on Mount Scopus, and occupies it to this day. During the 1948 Independence War, the school and its accompanying hospital (Hadassah Mt. Scopus) were cut off from Jewish-controlled Jerusalem, leaving the mountain as a garrisoned Israeli outpost in the midst of Jordanian territory, which it remained until the unification of Jerusalem in 1967. The areas around Mount Scopus, particularly Ammunition Hill, saw incredibly fierce fighting during that year's Six Day War. The Hebrew University's massive tower atop the mountain dominates the Jerusalem skyline.
Visitors to Mount Scopus can still enjoy the views of the Old City that gave the mountain its name, the Dome of the Rock shimmering in the sun atop the Temple Mount. Unfortunately, it is difficult to gain access to the Hebrew University's campus if you are not a student or an invited guest (due to security concerns), but the area still offers other attractions. Down the road (Etzel Street) from the university is a British military cemetery and memorial, the final resting place of several hundred fallen soldiers from World War I, which offers an opportunity for quiet contemplation. Going further past the traffic circle and up the hill takes you along the Hebrew University's Idelson dormitory, and two falafel stands operated by the Arab residents of the French Hill neighborhood. Jerusalemite recommends the further of the two stands (French Hill Falafel), as the other one is attached to a dentist's clinic of the same name, which conjures images of a dentist running back and forth between his deep fryer and drill, and is rumored among Hebrew U students to cause stomach upset. Further along still you'll see off to your left the French Hill shopping center, which includes a grocery store and several small restaurants and cafes.
At the end of the road are the gates to the Arab village of Isawiyya, a notorious hotbed of political unrest during the Intifada. Visitors are not always welcome. Before arriving in Isawiyya, turn left (the first left turn after passing the shopping center area) and follow the road's curve until you get to Tzameret Ha'Birah (about five minutes' walk), a neighborhood on Jerusalem's fringe characterized by its stunning views of the Judean Desert. The steeply terraced neighborhood offers a playground and a great number of impressive vantage points. Early risers can take advantage of a rare opportunity: at sunrise on a clear day, you can see all the way to the glimmering Dead Sea, forty minutes away by car.
Photo of Mount Scopus view courtesy of tmesis from flickr under a creative common license.