Great Information here. Also, check in with the NY R&P Association and local gun clubs. Plenty of Pistol permit holders on LI but not so much in NYC. Concealed carry is VERY rare unless affiliated with LEO/ agency. If you happen to be Active Duty and an Officer under orders, you may fall under special rules.
Many NYS shooters are military, active and reserve, and LEO's active and retired, so the company should be good. Weekly indoor competition and frequent CMP Excellence In Competition matches. Dutchess county has monthly "Precision" Pistol Matches (formerly Conventional Pistol). If you are in Northport, the Gold Coast reference is accurate, and you are about 30 miles from the Riverhead range near the former Grumman field (they test drove the F-14 there). They had monthly outdoor matches and shotgun, rifle and running boar there many years ago, and may still.
Born and raised in upstate (Binghamton) area, obtained my CCW from Chenango County Sheriff a long time ago, then found that Suffolk County would not recognize that NYS issued document. Left the state in 1991, but return to the in-laws periodically, and even shoot there competitively occasionally since 2001.
Good Luck, and thank you for your continued service.