A change to 16" wheels with tires that have a higher sidewall might help to soften the blow when you hit NY potholes. The roads up here in Ontario are pretty bad at the best of times, so I can sympathize with your feelings about the harsh ride over broken roadways.
There's another thread on here that details every tire and wheel size combo that should fit the CX-3. From the chart in that thread it would appear that a 225 / 60 - 16 is the one that is closest to the overall size of the OEM.
I have 17" rims with slightly higher profile winter tires and they seem to offer some softening of the impact over poor roadways. However, the suspension on the GT model is going to give you a firm ride even with different tire and wheel combinations, so you will still be aware when you have hit a pothole.