I'm so jealous! Akumal is one of my favorite places and we go at least once a year. We usually stay in a condo on Half Moon Bay. Ahhhh.
There aren't that many restaurants in Akumal, so here's the list. Unfortunately, in Akumal itself there is no actual Mexican restaurant. Always seemed odd to me, and I really wish there was one. But, most restaurants do have some Mexican or Mayan or Yucatan items on their menu.
La Lunita (Half Moon Bay at Hacienda de la Tortuga) - tables right on the beach, good service and food, candlelight, moonlight, starlight.
If you like Italian Que Onda, on the way to Yal Ku Lagoon does great homemade pasta and it's in a nice garden setting.(not beachfront)
La Cueva del Pescador - Akumal Bay, best seafood and super strong margaritas. They can also take you out fishing then cook your catch.
Turtle Bay Bakery & Cafe - Akumal Bay, hands down the best place for breakfast. Good bakery (get there early), and they now serve dinner 6 nts/wk during high season. Dinner was very good, but on the expensive side especially when drinks were added. Also serve lunch.
Lol Ha - Akumal Bay. Used to have a great selection of Mayan and Yucatan specialties, but has gone more continental (American and European standards). Has outside and inside dining. Good for lunch and ok for dinner.
La Buena Vida - Half Moon Bay, great happy hour, good guacamole, salsa and quesadilla and nice view for sunsets. Dining room upstairs from the bar has a good menu, but quality and service are hit or miss. Lunch, everything from the burgers to grilled sandwiches will most likely have mustard and/or mayo, and may or may not be hot. Again, hit or miss.
For something quick there's also the Loncheria beside the Super Chomak and Emelda's by the CEA. Lucy's has homemade ice-cream and I think she's also offering a small menu now too.
If you are renting a car you could head to Tulum, Aventuras, PDC or other areas where you'll find more restaurants.