Sure you could buy a tazer, or a real gun-provided you are (or get) properly trained on its safety, and use. And provided you can get licensed to carry concealed, across state lines. I would think if you are planning to stop at national parks this may prove problematic (very strict weapon regulations).

For personal defense I would recommend sprays (mace/pepper). Allows further distance and more "shots" than a tazer. Is non-lethal. Works against animals (again non-lethal).

a) Use your brain-don't get into a bad situation.
b) Use your legs-walk away from a bad situation.
c) Use your mouth-don't make a bad situation worse (but call for help as needed).

-Also, I wouldn't be concerned with being "attacked" while touring. Perhaps a bit of a concern in some Metro areas you might visit for "touristy" sites-only because you may not be that familiar with "bad" parts of town.

It's the same all over the world-not just in the US.