I also agree that 5 Brothers is the place to go. You should be aware, however, that the Cuban sandwich you'll get at most places in Key West, 5 Brothers included, is different from the Cuban sandwich you'll get in other areas like Miami. Most places in KW call their sandwich a "Cuban mix," and the main difference seems to be the addition of lettuce, tomato, and mayo, as well as sometimes salami. Growing up in KW, I was rather surprised to learn that a Cuban sandwich everywhere else was different. At 5 Brothers, the medianoche or midnight is closer to what most places call a Cuban sandwich, the difference there being that it's served on a smaller sweet roll rather than Cuban bread. Both are great sandwiches, and sometimes I think I like the medianoche more. Also worth trying at 5 Brothers are the bollos, little fritters of black eyed peas and garlic. Their ox tail lunch special is also very, very good. And the coffee of course: order a buchi and you'll get a tiny shot of espresso with sugar, called a "cafecito" outside of KW, it seems.
FYI, the 5 Bros. up the keys still makes molletes (Cuban bread hollowed out, stuffed with picadillo and deep-fried).