Where in Duluth?

In an effort to tease out a hint, I will guess that this is attached to a long-defunct business.

Nope. Not defunct.

Looks like this is gonna be a real stumper. As Paul said, this business is still in operation. This signpost, however, is not.

Can't remember the name of it, but is it outside the motel on Cody Street up by the ramp to/from Interstate 35? 

Direct-dial phones would have been an important selling point for a motel, circa 1965.

I'm going to guess that blue motel on the hillside just off of 6th Ave. E., up the hill from the Coop.

Akjuneau has it. It's the Allyndale Motel just off Cody Street.

I'm not sure if the sign belongs to the Allyndale or not, but isn't it on the property of the Cody Inn Apartments?

That could be the case. It's on the corner of 68th & Cody. The sign above the telephone sign reads "MOTEL," but doesn't indicate any particular name of a motel.

I think the sign is either to indicate "you can turn here to get to the Allyndale" or it might be a relic of the Cody Inn being a motel before it was apartments.

My family always called that the No Tell Motel because we never knew the name.

To further clarify:

The Cody Inn Apartments was the Cody Inn Motel during the late 1990s, and was the Tru-Vu-Motel going back into the 1980s and 1970s. 

So you might say the sign in this photo likely has nothing to do with the Allyndale Motel, since it's on the Cody Inn property ... however ... in the early 1990s, between its era as the Tru-Vu-Motel and Cody Inn Motel, the building was an annex of the Allyndale Motel. (This according to various Duluth city directories).

The sign is probably from the Tru-Vu-Motel era, but I'm just guessing.