Anything but
tobacco, menthol, mint or wintergreen e-liquid is technically illegal in NY. You could probably get fined and have your vape taken away by customs.
I'd bring only cheap gear with compliant liquid to be safe. You can always track down flavored liquid in NYC after you're done with customs (ask vape shop workers for it; they won't keep it visible).
Another way to get flavored juice is to go to Connecticut. It's legal here, and very close to parts of NYC (e.g. ~20min from Yonkers to Greenwich, CT by car, maybe a subway even goes to CT), so that could potentially be another viable option for you.