If your handheld is a typical 2 meter or 440 radio, and if you are in range of a repeater, you can talk for dozens or hundreds of miles, using that repeater. But that is not always a given...if there is no repeater that you can hit from deep in a forest canopy for instance...then you might be out of luck.
But yes, ham radio typically has pretty good range, and if you are willing to study and upgrade your license then you can use the HF (high frequency) bands and with the right equipment, you can talk all over the USA or all over the world.
A reasonably intelligent and motivated individual can study online for a week or two, and when they can pass the online test at least 80%, they can walk into a testing facility or hamfest and be reasonably sure of passing the test (70% passing grade)
It's a good, interesting, useful, and lifelong hobby.
Good luck and keep us posted, or feel free to ask questions here.