I think "cafeteria" as used by outfits like S&W Cafeteria, etc. would have been somewhat close to the idea of "a place where you get what is available", but the

I think "cafeteria" as used by outfits like S&W Cafeteria, etc. would have been somewhat close to the idea of "a place where you get what is available", but they have - as you say - mostly gone away. I suppose a "buffet" would also be close, in that you get to pick your food, but you're picking from an array of pre-prepared items with no room for variation for the most-part. As opposed to "made to order".