Wow! A true - hidden - gem. The place is literally hidden with no external signage that I could see. If you enter the Statler Arms Apartment building off of Euclid you have to walk deep inside through the lobby, past Juji's Cafe on the left and almost to the elevator bank till you find this spot just jutting out into the lobby on the right. The shop is much closer to the E13th St. entrance.
I was the shop's only customer at the time. The barista was very friendly. There was an ad for pumpkin something on the wall and I asked if that was flavored coffee. When she told me it was a latte and I said I would take it, she first offered to just add the pumpkin syrup to a coffee - very considerate and attentive to what I might want.
I got the Pumpkin Carmel Pecan latte ($3.95, medium) which blew me away. I was honestly expecting not to like it, but it ended up being one of those drinks that you guzzle down in 5 minutes audibly moaning as you do.
The fancy drink menu was limited, but clearly they do what they do well. They also have smoothies. There was a small clear case on the counter, but at 3:30pm it was empty so I guess go early if you want whatever goodies may have been housed in there.
While there was no seating seemingly dedicated to Copper Moon there were some seats across the lobby from Juji's Cafe which appears up for grabs. Very quiet interior at the time of my visit, though I suppose when Juji's Cafe gets busy you lose that silence.
Also currently when you check in on Yelp you get $.50 off your drink. And when you pay by credit card (they use the Square app) you get an email receipt which at the bottom tracks your number of visits. After 10 visits you get $1 off your next purchase! Neat!