North Carolina laws are screwed way up. You can possess and own a gun (as a non-immigrant) but your can't (legally) buy one in North Carolina. You have to be a citizen or a permanent resident alien (with a green card) to purchase. HOWEVER, you can travel to one of the gun shows in Virginia, or many of the flea markets) and buy a gun. You cannot buy one from a delaer, as you would have to fill out the 4473, but you can purchase one from an individual. This isn't illegal, just the way it is. Even if you purchase a handgun from a non-licensed person (private sale) you still have to get a permit from the N.C. sheriff, and will have to prove residency or citizenship.
Now so far as carrying you gun, you can do that in North Carolina openly. We have no law prohibiting open carry of an unconcealed weapon. But you can't carry it in Cary, on school property (college) and other places indicated in the NC firearms laws.
You won't be able to get a concealed handgun permit (in NC) without being a permanent resident alien or citizen. I don't know about other states permits. I know that you cannot get a non-resident Virginia permit unless you are a citizen or a permanent resident alien.
If was gonna make a choice like yours, I'd go for ARIZONA. Vermont also allows open or concealed carry without any formal red tape. If you aren't a crook, you can open or concealed carry in Vermont.
I'm not a lawyer, so double check the above before making any decisions. Open carrying in NC can get you some strange looks from others and some places might ask you to leave, but it is not illegal.
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In the beginning, the patriot is a scarce man -- brave, hated, and scorned. But when his cause succeeds, the timid join him. For then, it costs nothing to be a patriot. -- Mark Twain