This depends on several different factors. First, of course, it depends on your schedule and when you can travel, perhaps including your children. But you should also consider the weather in Israel, what kind of experience you are looking for, costs (peak and off-season), and the calendar of Jewish and Christian holidays (the latter relevant because of outside tourists; the Christian population in the country is very small, and Christian holidays are not observed in Israel). Let’s start with the weather. Israel has only two primary seasons with “shoulder seasons” in between.
The summer is from April to October. During that time, it is warm to hot and sunny every day and almost never rains. Sometime in October or November, the “winter” begins with the arrival of the rains (very welcome in this parched land), and this lasts until sometime in March or early April. We had a surprising amount of rain on one October visit, unusual for that time of year, but that is rare indeed and we still were able to do and see nearly everything we wanted. If you are watching costs, November can be a less expensive time to visit, but the weather can be less predictable. Of my five November trips, I had flawless weather and even unusually warm weather for four of them; on one, I had quite a bit more rain, including major blocks over several days and temperatures in the 50s F (low teens C).
In November, take light sweaters and a light jacket, but remember to take hats for the sun, which can still be intense. March can also be quite nice, with wildflowers blooming in the countryside after the winter rains. I went in March for my last trip and loved it, despite some rain—that green carpeting what will soon be barren desert hillsides! If you go in December through February, know that the weather can be quite cool, wet, and even nasty. Snow is rare (and only in the higher elevations, such as Jerusalem), but temperatures in the 40s F (single digits Celsius) with rain are common— and many places lack central heating, making the room cold!
From May through mid-October, rain will not be a problem. I have made three trips in late June, and it can be hot, but not generally brutally so. May is a wonderful time to go, unless like one friend you have allergies to olive tree pollen, because they’re in full bloom then. Temperatures are generally in the 70s F (high 20s C) every day except occasional heat waves, and the evenings are just delightful. The temperatures were also quite nice in October, though more variable. Even in the summer, we have sometimes needed a light jacket for evenings in Jerusalem, which remained lovely. July and August will be quite hot, even brutally so, and more crowded, because that is when families travel. The climate is basically the same as Southern California. At the Dead Sea or Eilat, though, it is warm to hot year around, and extremely hot in the summer, like Arizona. Despite the hot weather, summer is peak season for Israel travel, with more crowding, higher hotel prices, and even minimum stays at some hotels. Unless July or August is the only time you can go, I recommend avoiding it. You will also find peak prices and crowding around the major Jewish holidays, especially Rosh Hashanah and Yom Kippur through Sukkot and Simhat Torah in the fall, Passover in the spring, and Shavu’ot in the early summer.
In Jerusalem in particular, prices also go up around Chanukah/Christmas and around Easter, which is usually (but not always) the same week of Passover. (And remember, there is the Latin/Western Easter and the Orthodox/Eastern Easter—and they can be the same or different Sundays! In sum, my favorite times to visit Israel are from late April (after Easter and the end of Passover) through May, and late October (after Simhat Torah—search Google for the date in any particular civil year) through mid-November, with a recent affinity for green March. But you can have a good trip to Israel in any time of year.