is sleeping in car for few hours near Tell Aviv airport wise?

Are you looking for a room with a bed, or just a place for a few hours' shut-eye? If the latter, why not just sleep at the airport? You'll hardly be the only ones doing that. Tel Aviv airport is always full of people sleeping before catching an early flight, and it's safe. By "bathroom" do you mean shower/bathtub, or toilets? No to the former, yes to the latter obviously.

There are no hotels or hostels near the airport. The closest ones are in Tel Aviv (the city).

yeah, just a place for a few hours shut eye. Personally I have done it before in many countries as I find a folded back car seat far more comfortable to sleep on for a couple hours than a tile floor of an airport. I had planned on just sleeping in the airport, but figured if it was safe I'd prefer the car :)

Sleeping in a car isn't something I've tried - anywhere on the planet - but I don't think it's a good idea near Ben-Gurion Airport. You would probably be considered a security risk (in a very security-conscious area), and at the very least woken up by the police several times during the night. Also, traffic is very heavy all round that area, so it won't be quiet.

Sleeping in the car inside or near the airport is a no-no, it will look suspicious to the police. Sleeping in the airport is also a no-no, it's very noisy and there are people everywhere, not really the place when you can get some sleep. I'd suggest you rent a cheap room in Tel Aviv, get some sleep and then drive to the airport. It's possible to find a double hotel room for around 80USD.

From the arrivals hall, go down a level, to outside the synagogue and opposite the car hire desks (I do realise it's not an obvious combination). That area is relatively quiet, you can stretch out, and you will not be moved on. The cleaners and the security are constantly attending to their respective jobs, but will not bother you. Toilets and wash basins are obviously available. I am not saying either of you are going to enjoy a deep refreshing sleep, but at least you can chill out.

But by 02.00 if the you may be allowed to go airside, for your 05.00 flight. Loads of flights leave that early, you may be suprised at how busy the airport is by 02.00, with people arriving to catch outbound flights. Once you are airside, there are cafes and retail units, and more importantly better seating.

Thanks for all the input. I think I'll just stay at a hostel in Tel Aviv for a a few hours. One other question. Is there a 24 hour gas station near the airport to fill up at 1am?

There is a gas station at the airport and i'm 99% sure it's open 24/7.
If you do sleep in your car, then you could try doing it on a random residential street in a small town near the airport like Shoham or Modiin. I would say there are no safety problems but there is always a chance that you'll have the police or a neighbor knock on your car window in the middle of the night.
Have a look at this map for reference. It shows Shoham-gas station-Airport Car Rental:
http://g.co/maps/bv37d

Here is the map for Tel Aviv-gas station-Airport Car Rental
http://g.co/maps/2kqpz

you may be suprised at how busy the airport is by 02.00, with people arriving to catch outbound flights.

Absolutely. The place is packed then. There are probably more flights leaving between 5 and 6 a.m. than the rest of the day put together.

One woud think that you woudm be far more comfortable at the airport. Jutsreturn the car and check in