You might want to price it also. At least in Hawaii, I've noticed that the (mostly) PADI shops charge 2/3rds as much for the referral dives as taking the whole course costs. You might find Florida a cheaper option (competition) also if you're going to be in the area before your trip
Is there some reason you have to be NAUI?
There must be 100?+ PADI instructors in NYC. I'd have to think all the shops have indoor heated pools also. Even if you don't have time to do the cert. dives they can just refer you to a PADI shop at your destination. A PADI shop near me offers referral recommendations based on shops they've visited/have a relationship with.
Also if you really don't have time, sign up for the e-learning and shorten the class time in NYC even further. I'm not sure you'd even have to go to a PADI shop at all in NYC if you did the e-learning dives on vacation - maybe you'd have to burn a day in class first while there for skills training - I really don't know exactly how that program works.
Welcome to PADI eLearning
You're probably looking at 2-3 days on the referral - no one does all 4 dives the same day.
I'd start with the destination shop and work backwards. Or a local PADI shop. If they do e-learning - there's also a referral code they give you so they access your online records. I'm sure there's some part of your course fee they get also.