I got my visa within 5 minutes in the airport. (curiously they charged me 30USD while the visa sticker says 15USD)
This has probably been mentioned but Israelis do not need a visa.
I ended up spending a very leisurely day out and about in Istanbul, We saw a few Mosques, the shuk (wow! even larger than Marrakesh) the Palace, the garden etc. (we did not make it to the Jewish quarter unfortunately) For the record, I saw a Jewish couple walking around with a kippa.
Forget cabs, Metro is quick and effective. The Tram is nice too.