La Unica:
It's a market, it's a cafeteria, it's Cuban and it's Colombian/Ecuadoran. Still one of the best bodegas in Chicago, here's something I wrote about it a few years ago:
La Unica: I grew up in Cuban neighborhood and I find La Unica to be quite authentic, for better or worse -- down to the odd, gruff owner at the checkout stand (asked if he carried Presidente beer, he shouted "we don't cater to Dominicans here"). The cafeteria has very good garbanzo soup, made with impossibly bright yellow Bijol (a commercial anato derivative) and the full panoply of deep-fried Cuban finger foods (papas rellenas, yuca rellena, empanadas, tostones, maduros, croquetas etc.). Best is the real cafe Cubano, dark and thick with sugar (like iced tea in the South, there's no such thing as unsweetened Cuban coffee), served in a styrofoam cup with a side of pill cups to use as shot glasses for the cafesitos. Sandwiches are pretty good, including, I think, the idiosyncratic croquetas preparadas (croquettes with saltine crackers and pickles), although I have yet to find a great Cuban sandwich in Chicago. While the store is truly Cuban (we go just to buy Royal Violets brand baby cologne; don't ask), the patrons are not. I see many Mexicans, Colombians, Ecuadorans, etc., and saw a good sized group of Brazilians last time I was there. Great mix. The menu makes several Colombian/Ecuadoran accommodations, as mentioned here previously.
Cafeteria Marianao/Cuban Coffee
Two places in Chicago do cafe Cubano correctly -- Marianao (named after a beach in Cuba) and La Unica (the grocery store on Devon). Cafe Cubano without as much sugar as possible is inauthentic. If you have to add your own, it's too late. This is because the sugar should be added, ideally, when the hot water meets the coffee, permitting the super-saturation that you describe. The very best cuban coffee is made not with an espresso machine, but with a sieve -- more specifically, a finely woven "sock" hanging on a metal ring, in which you put ground coffee and sugar then hot water ["manga" or "colador," lit. sleeve or strainer]. I have not seen this contraption in Chicago, and it is becoming rarer in Tampa and Miami. [Though it can be bought at La Unica and places in Humboldt Park.] The little pill cups are authentic, although one should cost about 25 cents. Typically, an order comes in a short styrofoam cup [a "colada"] with a stack of the little clear ones on the side. While on the subject, I must thank Gary for turning me on to Marianao, which apparently was sucked up from Calle Ocho during the hurricane and deposited on Milwaukee Ave. intact. It's the real deal, down to the little takeout window and counter. Also, it is the only place I have found that does a proper cafe con leche and Cuban toast. (The toast is pressed on the plancha (sandwich press) with lots of butter; dip the toast into the sweet cafe con leche and watch the world go by.) Other places that have decent Cuban food (e.g., the Ambasador, Cafe 28 ) don't seem to get the coffee right.