I came back this morning from the Airport at 0530 AM. The price for a taxi is at this hout (higher because it was still night fare) 112 shekel + 5 shekel airport tax + 3 shekel for each suitcase. During day time the basic price is lower. So one an expect to pay 20-25$ for a taxi.
I asked about Jerusalem of course. The basic night fare is 212, day time is 188 shekel (not sure) plus the tax and suitcases.
These are official fare by the ministry of transport.
As fot Tel Aviv, If one takes the train and later a taxi he won't save much money, but it will take much longer and less comfortable. The price for the train id 12 shekel, taxi will be 25-30, total in $ will be about 10.
The train is great to travel to beyond Tel Aviv, like Haifa. For Jerusalem one has taxi or Sherut.
To get to the airoprt from Tel Aviv - I took a taxi, it was at 0600 AM and it was 95 shekel. I used Moniot Azrielli (never used them before) phone number 03-6081333