Just west of the Kennedy, on Chicago Avenue is one of the best Cuban Restaurants in Chicago.  Habana Libre is a great Cuban BYO in the Noble Square neighborhood.  Although I haven't had anything bad on the menu, my favorite is Arroz con Pollo.  Order it the minute you step in the door as it's made fresh and takes time to prepare.  The massive plate of some of the best Arroz con Pollo is well worth the wait.  the best part is the leftovers that taste just as good the second time around.  One downside of serving tasty and inexpensive food,  is that word gets around.  This place has become very popular and the waits on weekend nights can be up to an hour.  My advice is to make reservations on the weekends and come early.  Or, maybe skip weekends altogether.  Habana Libre - 1440 W. Chicago/ (312)243-3303