I don't know that I would move *just* because of gym at that point; but if you are in a position that moving in general is a possibility I would consider looking into other areas of the country that you might want to live in and I'd include gyms as one of the things on the "needs" list.
For us, we *don't* move because of gymnastics. We have a cabin about 1.5 hours from our house. We'd love to move to the cabin full time. But... all 3 kids are in gymnastics. Near the cabin there is a decent gym for girls; but we'd have to do a 45 minute, backroad, curvy, mountain drive to get to the only gym nearby that has boys. And I have a kid who gets horrible motion sickness. So that just wouldn't work. there are other benefits to our current situation - closer to my husband's office (if we moved to the cabin he would likely keep an apartment so that he could just stay down there if he didn't want to make the drive), I'm very happy with the school the kids currently go to... But gym is one of the main reasons we don't live at the cabin year round.
For you, are you only able to consider region 1? I figure if you can consider that broad of an area, why not open it up more. I imagine there are LOTS of gyms to choose from in TX plus the COL is very reasonable. I know in GA there are a lot of gyms with boys teams and the COL is very reasonable. Plus, depending on the industry, there are lots of job opportunities in the Atlanta area. I guess that if I were considering a move like that I'd make sure I was looking at all of the options.
I do think that there are many reasons to move other than job. We would love, love, love to move to MT or WY. Our kids are just as passionate about down hill skiing as they are about gymnastics and I'd wager more natural with skiing. They get very few opportunities to ski down here in the South though. ;-) The quality of life that we think that our family could possibly have overall in MT or WY did have us seriously looking into moving (to the point we went out and looked at properties); but in the end the difference in COL was more than we could get over (houses are WAY more, jobs pay less). So for now we just continue to go out for our annual ski trips and we have found the smaller town way of life we like by buying the cabin and being there as much as possible. (We are able to own a nice cabin AND a house for less than most people pay for a small house in CA!)