Any suggestions for private car/shuttle transfer from IST to Beyoglu?

There are numerous taxis always right outside the main exit, just to the left as you walk out. Usually there is not a long line. There are also private / executive taxis just to the right as you walk out. They cost about twice as much, but the cars are nicer and there is no wait. I have also used a pre-arranged private car but it ended up being quite a bit more expensive, and involved a longer walk to the parking garage… Lux Taxi Istanbul +90 (530) 115 61 04

But again I would just use the executive taxis at the airport.

Also stop at the ATM to get cash before you leave the airport as most taxis say they take credit cards, but my experience is usually their machine isn't working and I end up paying with cash. There are 3 or 4 ATM's located by the exit, up the escalators close to the baggage lockers.

There is a service where you can get a pass to all the sights and includes airport transfer. It's a great deal. You also get access as well to get local advice. They immediately respond to texts. Extremely helpful and very good value. Getting to the sights from a hotel is easy. Getting back can be challenging. The cab drivers will definitely try to rip you off but because of the exchange rate it actually involves very little money. Istanbul is a great city.