There are three parts of speeches attributed to "down" in the dictionary: adjective, adverb and verb.
I understand , that at the bar is a sub phrase and a prepositional phrase. I don't know the rules of how each type of phrase is allowed to be built and I don't know where to look those rules up. Maybe a prepositional phrase can follow both an adverb and an adjective or maybe only one of them. Maybe some phrases are ambient and can be both types , but I am just guessing.
The whole sentence, wherein I found the phrase is:
Plenty of seats down at the bar