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NH Fish & Game posts a list, it is almost entirely private membership clubs.There are many states that have public state run ranges like Penn, CT, many others. The Pittman Robertson money is used for things like this.
... I'm not sure what NH has, if anything.
Even in New Hampshire, where the towns have limited options to restrict shooting, it's rare to find a public range or even a non-posted sand pit.Very few towns will post or show people where on public land they can shoot, because in general, people leave trash, shoot things they shouldn't, and liability. Mostly gone are the days where you can find a sand pit and blast away. I'm sure it's still out there, but it's not the norm anymore.
Grew up in Dorchester... many friends & family still live there... plenty of shootings on public property there...I understand Lowell encourages that as well.