Rachel drives Lorelai to the old abandoned inn, The Dragonfly. I don’t know where she got the car from, since she arrived in Stars Hollow by plane, and that isn’t Luke’s vehicle that she’s driving. Maybe Rachel bought her own car after she arrived in Stars Hollow.
Lorelai tells Rachel that she and Sookie have had the ambition of opening their own inn for a “couple of years”, and that they are saving up towards that goal. Unfortunately, they are not even close to their target amount, so it looks as if their dream will be deferred for several more years at least.
It’s hard to see how Lorelai can save toward the inn when she is (presumably) still paying off her mortgage, is saving for a trip to Europe, and saving to pay her parents back for funding Rory’s private school education. (She should also be saving for Rory to go to Harvard, but probably isn’t.)
Maybe if Lorelai stopped buying take away for every meal and multiple coffees every day, they could save faster?