Inn in each town has an interesting name pertaining to those who travel, i think (am almost positive!) the last Inn was named "The Rest of the Traveler". The author relates his experience, almost as if reviewing the food served in each town, and that the food gets a little worse along the way but still edible. The gist of the stories? Each place is serving parts of people, sending the parts it doesn't use to the next town along the way, hence the name of the final Inn visited. Driving me crazy trying to remember the title and author of this short. Can anyone help??!??
It's not a perfect match, but I wonder if this could be Curious Adventure of Mr. Bond by Nugent Barker. I read it in his anthology Written with my Left Hand.
In the story there are three inns The Traveller's Head, The Headless Man and The Rest of the Traveller. The eponymous Mr. Bond is the traveller. However Mr. Bond visits the The Rest of the Traveller first, then goes on to The Headless Man and finally The Traveller's Head, where he ... erm ... loses his head shall we say :-)