Testing a local charger would be wise if it's not too hard. The J1772 adapter is a simple device, it just passively connects the pins on one side to the pins on the other side, but there's always the possibility for something to be broken. It's unlikely, but if you can test it ahead of time you might as well.
Have you checked PlugShare to see what (if any) information they have on the chargers you plan to use? They often have good info, including general reliability and typical charge speeds.
Charge speeds can vary a lot. As others have said, 30A is pretty typical. Voltage can be anywhere from 240V down to under 200V. A lot of public chargers are on three-phase power which officially provides 208V, and sometimes they're on long/bad wiring runs which cause significant voltage drop. Some drop enough to cause the car to drop the amps as a precaution, too. The worst I've personally seen was a 30A charger which the car dropped to 22A, and which supplied something like 188V. This gave me about 14MPH charging. The best I've seen was 70A at 240V, although I don't have dual chargers so I could only use 40A.
(Strictly speaking, I did encounter one J1772 charger that was plugged into a 120V outlet, and so gave me about 3MPH. I don't know if that's really worth counting, though. Fortunately it was right next to a 240V/30A unit.)
Note that to estimate MPH of charge from the volts and amps, multiply V times A and then divide by 300. For example, 22*188 = 4136, divide by 300 and you get about 13.8MPH.