I think that we already discussed Israir in another thread, but I will answer this anyway. I was at the unveiling for their "new" Airbus 330. They only have one aircraft flying this route and it has significant issues when comparing it to the other three carriers that fly this route. Here are the pros and cons of Israir's New York service:

Pros:
Price

Cons:
Charter service (they change flight times all the time because they are charter, at TLV, charter flights get last priority for takeoffs)
One aircraft (if that aircraft has a problem, you can be stuck in either country for a while)
Service (really bad, in both Y-cabin and J-cabin)
Business class (yes, the price is lower, but it is a really dated seat that is not flat and reclines 145 degrees)
No frequent flier program (you pay so much for the ticket, and Israel is so far, why not get some credit for it?)

The overall feeling when flying Israir is that you are on a holiday airline (like Tuifly) but the difference here is that the flights are really long. Now, if you miss your flight with Israir, you have to wait a couple of days to get on another flight to Israel since they have no agreements with other airlines. Delta has the same problem that they only have one flight a day and if you misconnect, you might have to wait until the next day. Continental has at least two flights a day and El Al has the most non-stops a day (is it five now) and will fly you via Europe if you have a serious problem. By the way, leaving on the date that you want, there is availability from Newark on El Al. I use an El Al travel agent (732-367-8500). They can probably get you a great price for the days you want. Good luck with whatever airline you chose.