Why summer instead of all-seasons? Surely you'd like the option to be able to drive this car in snow, ice, cold, etc. should you have to, right?
BFG GForce Sport Comp 2 A/S Plus looks like a good choice. General GMax AS-05 are also very good for less $$$
https://www.tirerack.com/tires/tests...y.jsp?ttid=253
*IF* warmer-weather performance is so uber-important, *and* you *know* no one will have to drive the car in cold/snow/ice/etc, *and* you need to get 30k, 40k+ out of a set of tires then maybe a Ultra-High Performance summer tire is indeed what you want. In which case BFG Gforce Sport Comp 2 is your only good choice in that size. But it is lacking a bit in wet grip vs. others in that class:
https://www.tirerack.com/tires/tests...y.jsp?ttid=235
But in NY, why would you *need* summer tires *now*?
You might consider UHP all-seasons. For sure you could get tires with better performance in the wet. Which for a street car, for me, is the metric to go by. In addition to snow performance if you might have to drive in snow...
Regarding size, there are a lot more higher-performance tire options in 225/50-16 and 205/55-16 that would fit 16x7, but those sizes are a bit smaller in diameter than OEM for '15 Mazda3 (too bad they deviated from "normal" 25" diameter IMO!), so if not lowered it might look a little funny...