LORELAI: Hey, who are you on with?
MICHEL: The Cheshire Cat Inn.
The Cheshire Cat was the B&B in Portsmouth where Lorelai and Rory stayed on their road trip to Harvard [pictured]. Apparently there is also a Cheshire Cat Inn near Stars Hollow. Oddly, neither Lorelai or Rory remarked on this coincidence when they were at the B&B. Did the writer (Daniel Palladino) just run out of ideas for names here?
The Annotated Gilmore Girls 