The windshield washer motor on a 2003 Pontiac Grand Am SE is typically located
behind the front bumper cover, near the bottom of the radiator support. You'll likely need to remove some of the under-tray or lower parts of the bumper cover to access it. It's usually fairly close to where the washer fluid reservoir is located.
However, the exact location can vary slightly depending on trim level and any modifications. A repair manual specific to your vehicle year and model would give you the most precise location and instructions for access.