Because Jerusalem has a fairly high altitude—though only 40 minutes on the highway from Tel Aviv’s Ben-Gurion International Airport, it’s up at around 2,500 feet—it’s much cooler than down on the coast (or in the Negev Desert to the south). Summer brings a dry heat of around 86 degrees; winter drops down to the low 40s, and snow sometimes falls on the golden domes and cobblestones. In general, it’s bright during the day and cools off after sunset. The sweet spots are April/May and October/November.
More important to keep in mind is that many sights are closed, or have shorter hours, on Fridays, Saturdays, or Sundays, depending on which religion has its day of rest. On major Jewish holidays, you also have to deal with higher prices and schedule changes. Of course, as the center of modern religion, there’s never a shortage of religious festivals and processions—you can choose to avoid them or seek them out. And the cultural scene is vibrant, if more conservative than in Tel Aviv: The Israel Festival brings theater, dance, and world music every May and June; the Jerusalem Film Festival, in July, screens everything from local directors to Spike Lee; and Jerusalem Day, on June 1, celebrates the city’s 1967 liberation with memorial services, flag-waving dances, and hikes.