I'll be staying in Istanbul for three days. Is there any Pass that grants access to most places worth visiting and, perhaps, public transport?
Witt Hotels has some excellent information on Istanbul, which I have personally used and recommend reading. I have not used the Istanbul tourist pass or Museum pass myself as I did not deem it worthwhile for myself and based on the 'attractions' I wanted to see.
The tourist passes have options to add public transport.
Adult $75.00 USD, Child (Age 2-12) $35.00 USD
Adult $200.00 USD, Child (Age 2-12) $140.00 USD
Updated with recommendation:
Get the 3 day Museum Pass for 85TL and Istanbul Kart to get around. Its cheaper and the additional "attractions" on the tourist pass are quite tourist oriented and may be marked up a bit. You can definitely get cheaper local alternatives for the cruise/ferry etc.