Regardless of the time of day you decide to fly, the ticket price will remain around the same. Book flights from Fayetteville to Jerusalem as you normally would.
In terms of precipitation, rainfall in Jerusalem ranges from 0.0 - 5.0 inches per month. January is typically the wettest month, when rainfall can reach 5.0 in. June is typically the driest time to visit Jerusalem when rainfall is around 0.0 in.
If weather is an important factor for your trip to Jerusalem, use this chart to help with planning. For those seeking warmer temperatures, July is the ideal time of year to visit, when temperatures reach an average of 78.8 F. Travelers looking to avoid the cold should look outside of January, when temperatures are typically at their lowest (around 53.6 F).