The Isla Nena Cafe was a surprise we found just a little too late...and we didn't even actually find it, we were basically told to wait there for our flight. After checking our bags inside, the Vieques airport personnel told us we could wait at the cafe outside and they would come and get us when the plane was ready to leave.
We ordered cervezas as we sat at the bar under a tent decorated with Green Bay Packer paraphernalia. Interestingly, there was a pilot who joined us for a ginger ale, and airport workers came up to order lunch. Lymon, the very personable owner, placed orders through the window and told us about his Asian wife's special once-a-week dinners (apparently very popular among locals). We didn't even know the restaurant-bar had a name until he mentioned it. This was the Isla Nena Cafe that was rated highly on a few sites, but we didn't really seek it out, and at this point, we didn't have time to eat!
One thing that was pretty cool was that he gave us two of the traditional shots called chichaus before leaving. Even though we found the place too late to eat, I highly recommend checking it out. It's probably one of the most unique airport scenes I've ever seen, and with very friendly people.