State preemption (no local ordinances):
159:26 Firearms, Ammunition, and Knives; Authority of the State. –
I. To the extent consistent with federal law, the state of New Hampshire shall have authority and jurisdiction over the sale, purchase, ownership, use, possession, transportation, licensing, permitting, taxation, or other matter pertaining to firearms, firearms components, ammunition, firearms supplies, or knives in the state. Except as otherwise specifically provided by statute, no ordinance or regulation of a political subdivision may regulate the sale, purchase, ownership, use, possession, transportation, licensing, permitting, taxation, or other matter pertaining to firearms, firearms components, ammunition, or firearms supplies in the state. Nothing in this section shall be construed as affecting a political subdivision's right to adopt zoning ordinances for the purpose of regulating firearms or knives businesses in the same manner as other businesses or to take any action allowed under RSA 207:59.
II. Upon the effective date of this section, all municipal ordinances and regulations not authorized under paragraph I relative to the sale, purchase, ownership, use, possession, transportation, licensing, permitting, taxation, or other matter pertaining to firearms, firearm components, ammunition, firearms supplies, or knives shall be null and void.
Roadways:
207:3-c Use of Firearms, Bow, or Crossbow in or Across Highway Prohibited. –
I. No person shall discharge a firearm, bow and arrow, or crossbow and bolt from within 15 feet of the traveled portion of or across any class I through V highway of the state. This section shall not apply to those persons holding a special permit pursuant to RSA 207:7-a.
II. No person shall discharge a firearm, bow and arrow, or crossbow and bolt from or across the following public highways of the state including the rights of way thereof:
(a) Route 93 from the New Hampshire/Massachusetts state line in the town of Salem to the New Hampshire/Vermont state line in the town of Littleton;
(b) Route 89 from the intersection with Route 93 in the town of Bow to the New Hampshire/Vermont state line in the town of Lebanon;
(c) Route 95 from the New Hampshire/Massachusetts state line in the town of Seabrook to the New Hampshire/Maine state line in the town of Portsmouth;
(d) Route 293 from the intersection with Route 93 in the city of Manchester to the intersection with Route 93 in the town of Hooksett;
(e) Route 393 from the intersection with North Main Street in the city of Concord to the Concord/Chichester town line;
(f) Route 202/9 from the intersection with Route 114 in the town of Henniker to the junction with Route 31 in the town of Hillsborough;
(g) Route 16, commonly known as the Spaulding Turnpike, from the intersection with Route 95 in the town of Portsmouth to the Milton/Middletown town line;
(h) Route 3, commonly known as the F.E. Everett Turnpike, from the New Hampshire/Massachusetts state line in the city of Nashua to the intersection with Route 101 in the town of Bedford;
(i) Route 101 from the intersection with Route 114 in the town of Bedford to the intersection with Route 1 in the town of Hampton.
III. Any person convicted of discharging a firearm, bow and arrow, or crossbow and bolt prohibited under the provisions of this section shall be guilty of a violation.
Distance to dwellings:
207:3-a Prohibition. – It is unlawful for a person to discharge a firearm or to shoot with a bow and arrow or crossbow and bolt within 300 feet of a permanently occupied dwelling without permission of the owner or the occupant of the dwelling or from the owner of the land on which the person discharging the firearm or shooting the bow and arrow or crossbow and bolt is situated. Whoever violates the provisions of this section shall be guilty of a violation if a natural person, or guilty of a misdemeanor if any other person.
Compact portion of a town:
644:13 Unauthorized Use of Firearms and Firecrackers. –
I. A person is guilty of a violation if, within the compact part of a town or city, such person fires or discharges any cannon, gun, pistol, or other firearm, except by written permission of the chief of police or governing body.
II. For the purposes of this section, "compact part'' means the territory within a town or city comprised of the following:
(a) Any nonresidential, commercial building, including, but not limited to, industrial, educational, or medical buildings, plus a perimeter 300 feet wide around all such buildings without permission of the owner.
(b) Any park, playground, or other outdoor public gathering place designated by the legislative body of the city or town.
(c) Any contiguous area containing 6 or more buildings which are used as either part-time or permanent dwellings and the spaces between them where each such building is within 300 feet of at least one of the others, plus a perimeter 300 feet wide around all the buildings in such area.
Also:
http://pgnh.org/gunlawfaqs