In the first shot of the pilot, we see a sign with STARS HOLLOW FOUNDED 1779 on it. Stars Hollow is loosely based on the small town of Washington Depot in Connecticut, which incorporated in 1779. In the 19th century its industrial section was known as Factory Hollow.
However, Rory says that Stars Hollow is 30 minutes drive from Hartford, while Washington Depot is about an hour away from there, so it can’t have the same location. That distance might put it somewhere around the vicinity of the town of Wallingford or the city of Meriden.
The pilot of Gilmore Girls was filmed in Unionville, Ontario, and from then on at Warner Brothers in Burbank, California.