Before leaving for Hartford, Lorelai grabs a burger from a take-out place that is just a window in a wall, called KC’s Annex. It’s next to an art gallery that I don’t think we ever hear about. The burger is disgusting, according to Lorelai, and she is going to starve to death if Luke doesn’t get back soon (even though Stars Hollow has more food options than is economically plausible!).
This looks like the same take-out window where Lorelai bought fiesta burgers for herself and Max when they were on a date in Stars Hollow. (The menu is identical, and they both have a green window frame in a red brick wall). It might be where Lorelai and Rory buy their hotdogs, fries, and thickshakes that they bring to town meetings, as they aren’t from Luke’s.
It seems the food from KC’s is fine, as long as you know Luke’s is available as a regular option. The idea of being stuck eating nothing but KC’s is a horrible one. Lorelai drives past Luke’s, which is still closed, just as a reminder of what she is missing.