I went last year at the end of May/start of June with my family via United out of EWR. We returned 8 days later via United to SFO. Here are my thoughts:

1. Traveling up until late May is good. The day of the week you travel is key. If we had come back a day earlier, we'd have gotten Polaris to EWR, same if we departed a day earlier.
2. If you have Ritz Visa or another card with primary rental insurance, you can get a letter from them before you go to waive the Israeli insurance. It is very expensive. Take pictures of the car at return. Do a search on the old forum for horror stories.
3. During our time we visited Old city Jerusalem, Sea of Galilee, Nazareth, Dead Sea and Petra. I would recommend all.
4. El Al has a $75 ticket from Tel Aviv to Athens. Our plan was to stop on the way home for 2 days because the flights from Athens to Newark were wide open at the time. However, one of my sons got food poisoning at the Marriott in Petra and we had to stay 2 extra days there.

Awesome trip, would do it again. However, I hear it has gotten heated with the relocation of the U.S. embassy, so definitely check the state department and CIA websites for the latest advisories if you are headed to the Old City.