NYC has an effectively dead private gun culture, with noted effects on the attitudes of MYPD towards shooting. NJ has a weak but present gun culture, with enough of a market that the Dick’s Sporting Goods that opened up near me recently has a small but present firearms section, despite the difficulties in paperwork that any retail firearms operation in NJ faces. As I noted in comments at Uncle’s, the local county police range is making a range available for shooters once a week (no doubt at least partially because they took federal funds and must meet the public access requirements of such), and the current range manager wants to extent the hours and days. The range itself has a page on the county’s web servers (which is new).
One major difference? In NJ there is no paperwork required to possess a firearm in the home, range, fixed place of business, or in transit, and the paperwork to purchase firearms is shall-issue with minimal interactions with police and (relatively) low cost to the applicant. NYC requires a possession permit that is may-issue and very expensive ($235 or so per a glance at the NYPD page on obtaining a rifle permit), and there are ridiculous restrictions involved in actually transporting the firearm to a range. NYC requires registration of firearms, while NJ only recommends it (though handguns bought in-state will presumably be registered via the permit to purchase). Also, the permit to possess expires and must be renewed on pain of confiscation…
Thus, in NJ, to be a firearms owner you have to interact with the government once* to obtain a firearm as a resident (and not at all if you owned prior to coming to NJ*). So, if your interest wanes, you face no difficulties in retaining your firearm against the day it picks up. NYC, no such luck.
* – You need to provide a Firearm Purchasers ID card that matches valid picture ID to purchase “handgun ammunition” (undefined by statute, so many dealers require a card check for all ammo), and the FPID lists your address, so if you move you have to renew, which in some jurisdictions is treated as a new application.