Has anyone had experience using Uber to get a taxi from IST into the city? How was your experience?
I have not, but as I understand it Uber is only allowed to function via existing taxis, so you'll pay a premium for Uber versus using a regular taxi from the taxi stand. There are various taxi hailing apps (do a Google search).
I have used Uber in Istanbul, though not from the airport. My cousin ordered it through her normal Uber app and tracked my ride in the app to confirm my arrival. Even at 3am (post-wedding) the Uber picked me up within a few minutes. I didn't book the ride in my own Uber app (though I could have) so I don't know what the cost was. I've read the same as what CL mentions, that Uber will cost more than a taxi.