the route is
San antonio
Alamo
Austin
Dallas
Shreveport
Little Rock
Memphis
Nashville
Rugby, Virginia
Washington
Nazareth
New York
Phew - I'm tired
I assume that "Nazareth" is Nazareth, PA to see the Martin factory. Good choice. Along the way, visit Bluefield, VA to see New Graham Knives and their very wide selection of blades, all laid out in front of you in glass cases. Also, IIRC, Fender has a guitar facility in TN? Maybe in Sugar Hill? Most public gun ranges, at least the ones in the south, will have a variety of handguns and long guns that you can rent and shoot. Just make sure that the range has the capability of handling long guns. Some smaller indoor ranges are handgun only ranges.
Since you're going through AR, you might look up the address of the A G Russell store there and visit them while you're in the state. Don't know of any manufacturers along your route. BM, Spyderco, and CRK are in the west/northwest part of the country. Those are the only manufacturers that I'm really familiar with. Some of the other big names may have facilities along your route.
One thing you might try is checking the custom makers subforums here to see where some of the makers are. If any are along your route, write to them and ask if they mind you dropping in. You'll need to provide a date and time, or accept the date/time they offer you since they're busy people, and then make sure you're on time, but that might be a way to see how individual custom makers handle their craft.
Have a safe and enjoyable trip.