Cafe Habana

Cafe Habana offers some of the best Cuban food in New York City - including their specialty, Mexican grilled corn with cotija cheese.  That's not necessarily a Cuban dish (though they have amazing Cubano sandwiches and fish tacos as well).  This is a small,  busy place and you should expect to wait 20 minutes or more to get a table, but it's a place you should eat at before you die.

At the corner of Prince St. and Elizabeth St. in NoLita:

Cafe Habana