playgrounds are everywhere!
So getting around between different cities, a requirement to see the various tourist attractions, requires a car rental. Yes, there are buses and trains but I think convenience is definitely a factor with the kiddos. Then again, parking in big cities such as Jerusalem and Tel-Aviv is a nightmare, so I would suggest leaving the car in one place and using the light rail/local buses/taxis to get around. Both downtown areas are very walkable though.
on the light rail in Jerusalem
If we're on walking, then strollers are a must. Note that on a local bus, if you leave the stroller open you have to pay a passenger fare for it. It just so happens that our stroller, the Baby Jogger City Mini, was the most popular model we saw. People do a lot of walking so a good stroller is a necessary part of life. There are very few places where we had issues with the stroller that we needed a baby carrier, although I do think it is nice to have, especially if you make it to one of the many, many national parks.
The Mediterranean diet is very varied and full of fruits and vegetables. We had absolutely no problems finding foods that our kiddo would eat. Of note, Baby Boy loved the falafel, hummus, and Bamba! And pretty much every single restaurant we encountered had a booster seat for us.
stuffing his face at Max Brenner
Lodging, not particularly related to children, but I thought I should mention it, is very expensive. Especially in the summer, it's all about supply and demand and there's a lot more of the latter then the former. :/ In short, if you can get organized ahead of time, and survive the long flight over, you will have a fantastic time! Happy Travels!