You have three different tiers of services available to you in NYC
Use a local independent firm like Cego or Geneva or go over to Jersey and use one of the Gamberts. I think there are 3 of them to choose form. They all do their own work and one of them should offer the quality and service you like.
You could use a local outpost for a long distance service like Turnbull and Asser, made in England or Ascot Chang, made in Asia. These firms specialize in shirt making.
If you visit Bergdorf Goodman Mens store you will have a variety of MTM shirting options from the various brands/vendors carried there. They have a Charvet boutique on the first floor.
You could also visit stand alone flagship stores of Zegna, Brioni, Kiton, Attolini, etc. and see what they have to offer.