Fox on/at the Hearth works just fine, but the Fox and the Muffin is painful…

Happy Horse Inn & Livery
The Warm Bed In (or, if Inn & Brothel: A Warm Wolf Inn)
The Fancy Fox
The Hound's House (the Dog House)
The Huntsman's Home
The Bear's Bath-House

Ect ect… use your imagination.

As the pair walked up the street Sal pointed out various shops and landmarks. The last of these was an impressive gate that stood in their path.
"That gate leads to the inner keep and the duke's palace," he told the jaguar. "The Deaf Mule is also in there. It's the most popular pub in all the Keep."
He had no more then finished his explanation then he turned down one of the side streets. At the next crossroads they came to a large building with a sign displaying two hearths on it. It was an impressive building with the first story being made of stone masonry much like a tower would be. The next two stories were timber and plaster with a slate shingled roof atop it all.

So it would be below and a couple blocks over from that gate as I see it. Nothing is firm at this point so if needed it could change.

Would "Fox on the Hearth" be another good name? ;)

Description of the building
The main features of this inn are as follows. It is a very large building, 122' x 60' with an equally large stable behind it. Its first floor has stone walls with the second and third floors being half timber construction and its roof is slate tiles. The inn has 72 rooms that are for rent. About half of these are rented on a monthly basis to people who live and work in the Keep. The others are rented to travelers. Along with the guest rooms there are two large common sleeping rooms on the second floor for teamsters and other travelers needing just a place to roll out a blanket to sleep. There is also a pair of common sleeping areas in the attic for the serving staff. Another unique feature and one you wouldn't find in many if any medieval inns, is that the guest rooms that are in the central part of the building each have a hearth in them. The common room on the first floor has two hearths in it, one large the other small (somewhat like the owners) and it is this feature that is shown on the inn's sign. The common area has several large tables and a few booths along one wall. See the floor plan links below for details (some rooms are labeled for characters already staying there).

First Floor of the Inn
Second Floor of the Inn
Third Floor of the Inn
Exterior view of the Inn

Background to the inn and its owners
The inn is owned by Darion (AR) and Jami (TG) Goquen whose family has been innkeepers at Metamor for generations. Both were at the battle of Three Gates and made a last stand in their first inn. Darion's life was saved by being changed into a child and by his wife, Jami, being changed into a man who defended him. Their livelihood, the inn, was little more then a ruined shell by the end of the battle however. Darion, who had found a large sum of money on a Lutin commander he had killed, pledged to build a new inn that could also serve as a strong hold should the Keep's wall ever be breached again. Thus the current inn came into being and the Duke has allowed him to keep a secret store of weapons in the inn's cellar.

Darion is an energetic youth who is seldom seen without a smile. As with all children he seems to have boundless energy but he applies this to his work as an innkeeper. Jami is a large man who could easily be mistaken for a lumberjack. A sizable thick beard covering the upper part of his chest and his voice is a rich baritone. Jami is usually found at the bar in the common room where he directs the servants in their duties and makes sure those who have too much ale cause no problems.

Names that have been suggested so far are:
Companion Hearth Inn
Pair of Hearths Inn
Loving Hearths Inn
Jolly Hearth Inn

So, with all that information, does anyone have some suggestions for a name?