Things to See:
Old City (All 4 Quarters)
Western Wall (Wailing Wall)
Church of the Holy Sepulcre
Via Dolorosa
Dome of the Rock
Temple Mount
Mount of Olives
Machane Yehuda Market (The Shuk)
Yad Vashem (Holocaust Museum)
Dead Sea (An hour drive)
Masada (An hour drive)
Restaurants:
Hamarush
Sabich Aricha
Azura
Ishtabach
Piccolino
Bars:
Machane Yehuda Market (walk around here at night for lots of bars, hookah, etc)
Gatsby Cocktail Room
Mirror Bar
The Garden Terrace (Waldorf Astoria)
Rooftop Bars:
Rooftop (Mamilla Hotel)
Lodging:
King David Hotel
Abraham Hostel Jerusalem