There are several around! I even checked my email at an internet Kiosk at my resort (AKL). I did not pay that much attention, because it was easier in the hotel - but I did use one in the Magic Kingdom by the restrooms connecting Liberty Square with AdventureLand. They are probably available where most of the big phone centers are.
It was 0.25 per minute - with a $1.00 minimum. It was a dial-up connection - and not a very quick one either! (But it was enough to get my internet fix for the day!)
If you use an internet kiosk at MK, do you have to pay directly with a credit card? I don't see how you could charge it to your room. And also, does anyone know where there are internet kiosks in the Boardwalk/Beach Club area? How do you pay there?