Thumbs,
I'd suggest Wyoming as a good place to start. I say that because you aren't required to buy a hunting license there and you should be able to find some decent areas to shoot. Perhaps it's just a stroke of luck, but I've found it easier to find (free) places to shoot in Wyoming than other states.
If you know the route you're planning to take through Wyoming, you can look for co-ops or feed stores in the smaller towns. They usually have some suggestions to get you started. I've also called local chambers of commerce, because some of them have lists of land owners who allow hunting/shooting.
I hope this helps. Best of luck.