Murder -- Write With (AP) Style

Is it 5-feet-10-inch or 5'10 or five foot ten or 5 feet 10 inches?

It's the first on or the last one. AP Style, under dimensions:

Use figures and spell out inches, feet, yards, ect, to indicate depth, height, length and width. Hyphenate adjectival forms before nouns.

EXAMPLES: He is 5 feet 6 inches tall, the 5-foot-6-inch man, the 5-foot man, the basketball team signed a 7-footer.

Use an apostrophe to indicate feet and quote marks to indicate inches (5'6") only in very technical contexts.

Plus, did you need to refer to the North Point Inn by its full name in every reference? No.

In the first reference, a full name is necessary. But in subsequent references, something more generic and/or abbreviated would suffice, like inn (with the "i" in lower case) or the restaurant.

If there was a common and well-known acronym for the restaurant -- like MSU for Michigan State University -- then you could have used that. But in this case, there was not.