A portion of coffee that is consumed on a single occasion. A cup of coffee; some coffee; coffee. In American English, “a coffee” can also refer to an informal afternoon social occasion at which coffee and other light refreshments are served. “Jeff Israely’s journey was a little shorter—just round the corner from his apartment in Rome to have a coffee and a chat with his local barista, Vincenzo.” (Time, June 14, 2007)/”You grabbed the car keys and set off to your destination not worrying about whether your friends knew that you were headed to the mall, then to the grocery store, then you might stop for a coffee and, oh yeah – you needed gas, too.” ([Newport News, Va.] Daily Press, blog post, March 8, 2011). Google Ngram.
notoneoffbritishisms.com 
I say this all the time and get mocked for it. I was living in Europe and picked it up from my flat-mates. Even more egregiously, I say “a wine” which may be more a reflection of our tendency to drink a whole bottle rather than British influence.
I’m looking for a cuppa! Either coffee or tea…
This I can deal with. What makes me laugh every time is when Brits say they are “going for an Indian,” or “Shall we get a Chinese?” It sound like they are going to purchase a lovely Indian person to have dinner with, and even after two years in the U.K, I still can’t get over it.
And yet, I have read that in “The Love Song of J Alfred Prufrock” T. S. Eliot gives away his American background by writing “Before the taking of a toast and tea”, when a British person would have omitted the indefinite article.