Welcome. I'll be making the move from Texas, hopefully within the year.
Here are the basics of NH gun law:
-Unlicensed open carry on foot is legal.
-To carry a handgun that is both loaded and concealed, you must have a license. The license costs $10 for 5 years, is must-issue, and is issued by your town government (usually the police department). They must issue within 14 days of the application.
-To carry a loaded handgun in a vehicle, you must have a license. Open/concealed don't matter.
-No loaded long guns in vehicles (this is a hunting law, and people are trying to change it).
-There is total statewide preemption. Only the state legislature can regulate possession, carry and discharge.
-Here's the list of places off limits to carry: courtrooms. That's it, just courtrooms. And they have to store your gun for you while you're inside.
Of course, private property owners can tell you to leave. You can be charged with trespass if you refuse, but there's no enhanced penalty for carrying a gun.