Stars Hollow, the small-town setting of Rory Gilmore, a super in-sync mother-daughter pair whose rapid-fire, hyper-articulate conversations are often setting against the backdrop of their unique Connecticut village.
While it has become something of a cliché to describe a story's setting as "like another character," Rory leaves for Yale. What's more, there are plenty of (generally) loving references made by Lorelai and Rory about how only Stars Hollow could have residents as eccentric as Kirk, Babette, or Miss Patty.
Amy Sherman-Palladino has singled out a trip she and husband Daniel Palladino (who also served as co-showrunner for most of the series) took to Connecticut as the primary inspiration for Stars Hollow. This trip was made after Sherman-Palladino's totally improvised pitch for the show was accepted, but before she had clearly defined what it would be. As such, their visits to towns like Washington, Hartford, New Milford, and Kent influenced the shape of the show as a whole in way that is usually reserved for personal experience. Washington Depot in particular is home to an inn called the Mayflower Grace, where the Palladinos lodged during their stay and which served as the model for both the Independence Inn and the Dragonfly Inn, while the influence of the town meetings held in Kent can be felt in the way that Taylor Doose lords over Stars Hollow. Sherman-Palladino has even pointed to the Frog Hollow neighborhood of Hartford as the inspiration for Stars Hollow's name.
In addition to local specifics, consideration was also given to how Stars Hollow relates to the state of Connecticut as a whole. The most consistent example of this is the contrast between Stars Hollow and Hartford, where Richard and Emily Gilmore live. Owing to a very conscious decision by the showrunners, Hartford comes to represent the up-tight, old-money ways of Lorelai's family, whereas Stars Hollow, distanced from that kind of culture (by roughly the same mileage as Washington Depot is in real life), is a place where a tight-knit community can nurture and appreciate its own strangeness.
Of course, Star Hollow doesn't have a direct one-to-one connection to any of its source locations. Lines can be drawn to various points of inspiration, but ultimately it is an amalgamation of many different traits, brought to life by the wealth of quirky writing and acting on display on Gilmore Girls. And given the loving specificity of the show, it seems appropriate that Stars Hollow has so much life and character that it could only ever really exist as itself.