Veromonter, the answer is: it depends.
I ran into the same problem with having a RI CCW. No one has reciprocity (well, just a very few and it's not 2-way reciprocity). So I can get a Florida if I want, but there are a number of states that will not recognize it because it is not my state of residence. A number of the states will, some will not. You need to check each state to confirm.
I ended up getting a CT, NH, ME and PA license because they were easy and the places I generally go. I would like to get a MASS license but it's a little more difficult and costs $100 a year- and you have to reapply EVERY year. I just do my best to stay out of MASS if I can.