Just interested in learning the context behind a cup of "Joe". It seems weird that we'd use a proper noun to name a cup of coffee, rather than anything else.
Nice reference at Snopes says that a "cup of Joe" does not refer to
Josephus Daniels (18 May 1862-15 January 1948) (who) was appointed Secretary of the Navy by President Woodrow Wilson in 1913.
Snopes says it's not Daniels because the Navy was already officially dry at the time.
The article goes on to describe some of the possible linguistic origins "cup of Joe", such as Joe being the common man (and coffee being the common man's drink).
Snopes borrowed liberally from World Wide Words, and I would refer the OP to Michael Quinion's article. As a linguist, he has done an excellent job in ferreting out folk etymologies.
Slip me a slug of the wonderful mug / 'An I'll cut a rug just as snug in a jug / Drop a nickel in the pot Joe / Takin' it slow
I've just found (via Google Books) the following passage from The Princeton Alumni Weekly volume XXVII, No. 19 (February 18, 1927):
Speaking of Restaurateur Joe, that gentleman recently advertised that he had a brand of coffee, one cup of which would keep an exam-harrassed student awake all night. Dean Gauss commented on this with characteristic wit in the next day's Princetonian. He suggested that each morning throughout the academic year "a full cup of Joe's waking potion" be administered "to every undergraduate in good standing." The Dean, no doubt, has some morning lectures.
Given Princeton's prominence and influence in American letters and culture, I can't help but wonder whether undergraduate slang in 1927 might have become common parlance three or four years later...
The origin of the term is a bit nebulous. But it's believed to be a shortening of jamoke (a concatenation of Java and mocha).
See this article on Snopes for more information.