Horse and Four is a highly reputable inn located near the University.
In The Chronicle Edit
After Kvothe earns his talent pipes, he comes to an agreement with the inn's owner, Caverin, about playing music three evenings a span in exchange for free room and board, and two talents of pay per month. Kvothe finds the accommodations to be stellar, with remarkable kitchens and spacious rooms.
His stay at Horse and Four was short-lived. Ambrose arranged for the inn to be bought out, and subsequently fired Caverin, and hired a new owner who informed Kvothe that his services would no longer be required. Ambrose then proceeded to threaten all of the pubs in the area about hiring Kvothe as a musician, but eventually Kvothe ends up with an arrangement at Anker's. While Anker's was not as spacious as the Horse and Four, in hindsight Kote is happy that he ended up in Anker's. For although the crowds were not as wealthy as those at the Horse and Four, they appreciated him in a way the nobles never had.