Cuban Food in and around NYC
El Artesano is a lot of hustle and bustle, as lovessushi says, but it's actually a luncheonette with waiter service; they're well-accustomed to non-Spanish-speaking curiosity-seekers, too: http://www.eatingintranslation.com/2008/06/el-artesano-res.html
El Fenix is indeed the name of the bakery (it's where El Artesano gets its bread, our waiter told us); it's about two blocks north.
The "other street" that lovessushi mentioned seems to be New York Ave., which runs parallel to Bergenline, one block east. Apart from a corner eatery called Night and Day ( http://www.eatingintranslation.com/20... ), there's a bunch of other businesses I haven't had time to explore. Please report back if you find that second bakery!
El Artesano in Union City is a cafeteria sort of place - you can sit down but it's definitely a lot of hustle and bustle - awesome Cuban food and hot churros available as you walk out the door! There is a bakery somewhere along that side of the street - within a few blocks but I can't remember exactly where - it may be called El Fenix but I can't remember.
There is also a bakery on the street that runs behind Bergenline - so if El Artesano is on your right, the street will be the next one over towards the left if that makes sense - I can't remember the name or quite where it's located but if you get into the low 50's high 40's cross streets on Bergenline, turn and check out that back street and it's somewhere there (that doesn't make any sense, does it?)
There is also the Latin American Restaurant on Bergenline though it's not completely Cuban anymore, I understand it's still pretty good.
Isla is a good take-out/cafeteria place in Hoboken -
That's about all I know of (and I remember Rincon Criollo - I use to go there as a kid and eat maraschino cherries from the bar :-) (without the alcohol!)