The local beer is Orion, brewed in Nago on the main island of Okinawa. It tastes different from Orion sold in the rest of Japan which is made by Asahi. The other local drink is awamori 泡ç, which is usually 30% alcohol in Miyako. Much has been written about its potency and locals will tell you that it is good for you and doesn't give you a "bad drunk" waru-you or a hangover futsukayoi. Nonsense! It can be drunk in many different ways, but for starters try the orthodox: on the rocks, 2 or 3 parts water to 1 part awamori and drink it as you would any other 10% alcohol drink.
Miyako has its fair share of watering holes, so just ask around. It's also perfectly legal to head to the beach with your cooler and some fireworks. Just follow the golden rule and leave the place cleaner than you found it.