Welcome to New Hampshire, the most free State in the Union.
A few things need clarification; There is no CCW permit in the State of New Hampshire. We have a pistol license that allows you to carry a loaded pistol in a vehicle, and a loaded pistol concealed on your person. All other forms of carry do not require any permission from the State.
Relevant Statutes are RSA 159:4 for unlicensed carry, and 159:6 for your license application. By law, they have two weeks (14 days) to approve or deny your application. I received mine at ten days.
On paper, New Hampshire has suitability, but in reality is shall-issue.
In Manchester, the mall has a posted sign at entrances (I recall seeing one the last time I was there, about a year ago) that prohibits weapons. Whether this has weight of law in NH, I'm not sure. If you are OC'ing, this would be an issue, as security and anyone else can see your pistol. CC'ing, well not so much as no one would detect the pistol. Again, I'm not sure if signs carry weight of law so I would recommend adhering to them. You won't see signs often in this State.
As far as State law goes, I'm fairly sure the only off-limit area is a court house. Anything else goes. If this statement is not correct, I encourage anyone to chime in with a correction.
Good luck, and again welcome to NH.