EMILY: I wanted to know if you’d like a gift certificate for a weekend at the Birch Grove Spa.
A fictional spa. In real life, there are several luxury spas in Connecticut where Emily and Lorelai could have gone. The Mayflower Inn in Washington Depot, which provided inspiration for the Independence in Stars Hollow, has luxury spa facilities [pictured], but I think they were introduced at the inn a year or two after the date of this episode.
The Annotated Gilmore Girls 