1. The Israel Museum — Givat Ram
The country's national museum — Dead Sea Scrolls, the Temple model, and far more than a day's worth.
The Israel Museum is the largest cultural institution in the country and one of the leading encyclopaedic museums in the region, spread across a hillside campus at Givat Ram with archaeology, Judaica, fine art and design wings.
Two things bring most visitors: the Shrine of the Book, the distinctive white dome housing the Dead Sea Scrolls, and the Second Temple Model — a 1:50 scale reconstruction of Jerusalem in 66 CE that makes the Old City legible in a way no map does. Do the model before you walk the Old City, not after.
The archaeology wing alone justifies the trip, and the sculpture garden is one of the better ones anywhere. Allow a minimum of three hours; a full day is not excessive.
Good to know: Do the Second Temple Model early in your Jerusalem trip — everything in the Old City makes more sense afterwards.