Whirli, Wyoming is about as remote and empty a place as you are going to find in the continental US. You won’t have the same refugee problems as many other places, but Metro Denver and its 3 million people is only a tank of gas away from a good chunk of WY. They wouldn’t all head north of course but some will.
In the Northeast it is a very different story. The Boston to DC corridor has almost 50 million people. Half of those folks are within a tank of gas from VT so the Golden Horde is prominent in my thinking. As with my Denver example they wouldn’t all head to VT, but some would.
The situation will differ from region to region, but if the grid goes down nationwide, there will be problems everywhere. Some areas will be better or worse than others but all will have issues. Population density, climate, time of year, local resources, local culture, and ethnic/racial/religious mix will all be factors.
A complicating factor early on is that it will be difficult for any of us to fully know what is going on if the grid is down. I suppose we’d pull out our battery operated emergency radios to find operating radio stations that have real data, or perhaps turn to local ham radio operators. Assuming we do get good info quickly, most in our communities aren’t going to be as quick on the uptake of grasping the situation when the reality is beyond anything they’ve ever contemplated. For those reasons, there would certainly be a window when folks do stay put waiting for everything to go back to normal.