Since it's a Federal program, it should be acceptable across the U.S. However, if you are relocating to a cheaper cost of living area, expect your Section 8 voucher to be adjusted. Example: if you are moving FROM a high cost of living area (New York City, San Francisco, Washington D.C.) and moving TO a cheaper area (Arizona, the Midwest, etc.), Section 8 will lower the amount you receive. If moving from a cheaper area to a more expensive area, Section 8 will increase the amount.
Before you move, read and follow up on what the government is doing with Section 8. There will be changes coming soon.