Al's Mar Azul is definitely one of my favorite places to have a drink in Vieques. It's perched on a cliff overlooking the Caribbean Sea, with unbroken views of the ocean and horizon. You can see mainland Puerto Rico and Culebra Island in the distance - it's a gorgeous view.
The atmosphere is super-relaxed and friendly. You'll strike up a conversation with the bartender, a fellow patron, or Al himself, who's usually parked at the bar reading the paper. A native of Westerley, Rhode Island, Al is quite the character, especially on a raucous Saturday night.
Have a cocktail or a beer - Medalla is the best; it's a local beer and I believe just $2.50. Play pool, video games or darts, put some music on the jukebox, and sit outdoors on the deck or inside at a table. Make sure to check out the tiny Al's Gift Shop where you can buy a customized ice-scraper for your car. You'll be using it a week after you get back home, dreaming of your next trip back to Vieques!