I have a NH concealed carry permit which I believe is recognized in Arizona.
I do not believe it is recognized here. I rely on this chart: http://www.ccrkba.org/reciprocity.html
I know there is no reciprocity, but I do not think it is recognized either.
I intend to carry concealed most of the time.
There are several states that will issue you a permit on the grounds that you have one in NH. You MAY be able to use these to carry in AZ, if AZ accepts them. This is obviously a loophole, but you can use it as long as you are not a resident of AZ. Utah may be a good one.
When out hiking I will be open carrying.
I would always oc if the cc permit is not recognized.
When going to a restaurant or bar I will transition from open/concealed carry to locked storage in the glove box / center console (as I have a CCW permit is it ok for the handgun to be unholstered in the glove compartment?)
If the place does not serve alcohol for consumption on premises you can take it in. This eliminates most places, but you can carry in Subways, fast food, and other dry reastaurants. You can also carry in places that sell alcohol as long as they do not have a consumption licsense (like a grocery store or wall mart are ok)
If you have someone in the car with you the unholstered handgun in a glovebox or console could be construed by LEO to be concealed by your passenger, and they would get in trouble. The Driver's CCW does not cover everyone in the car, even if you are driving and its your gun. This is solved by bringing a cheap exta hoster and putting the gun in it inside the glovebox, (or you could just use your regular holster). WHEN A GUN IS HOSTERED AND IN THE GLOVE BOX, CONSOLE OR MAP POCKET IT IS NOT CONSIDERED CONCEALED. I know this sounds rediculous, but its the law. Look up ARS 13-3102 read it and print a copy of it to carry with you. you can carry a hostered gun out of sight IN a designated storage compartment in the car. So if I were you I would OC in my car this way even if my CCW were not recognized. BTW, this gun can always be loaded when carried this way.
I intend to visit the Pima Air & Space Museum, I assume as the tour of the boneyard goes onto USAF property I should keep the handgun locked in the glove box / center console of the rental car.
I think the air and space museum is private, but you need to look that up.