If you normally pick up prescription medications at one of the large pharmacies, such as Walgreens, CVS, Walmart, or Costco, they have stores in many towns across the USA and can readily fill your prescriptions.
If your favorite pharmacy is not represented where you might be traveling, any pharmacy will readily contact your home pharmacy and transfer and fill your prescription. If you have no refills remaining, the pharmacy will contact your doctor, but this may take a few days, depending on how quickly your doctor’s office responds.
A number of pharmacies offer a mail order service for medications.