In Akumal:
La Lunita (on Halfmoon Bay at Hacienda de Las Tortugas) - get a table on the beach. The coconut shrimp are always really good, and the fish that's cooked in foil w/ fresh veggies is also good. Steak w/ blue cheese sauce is usually good. Cafe La Lunita and pretty much any dessert.
La Buena Vida (Halfmoon Bay) - good for happy hour drinks and snacks and great views for sunset. Dinner and Lunch are hit or miss.
Turtle Bay Bakery & Cafe (in the main square across from Akumal Bay) - Excellent breakfast! Nice, but pricey dinner.
Lol Ha (Akumal Bay) - Used to be very good with a good selection of Mexican and Yucatan specialties, but it's gone more American and Continental and now our experience is hit or miss. There do have a jazz or blues band a couple nights a week, and dinner in the inside restaurant is supposed to be better. Haven't been recently so can't say.
Que Onda Restorante Italiano (near Yal ku) - nice, simple, homemade pasta dishes. A quaint garden setting, it's on the property of the Que Onda inn.
La Cueva del Pescador (main square across from Akumal Bay) - The best for fresh seafood and very strong margaritas. If you like fishing, make sure to talk to Carlos, the owner. He will take you out fishing in the day then cook your catch to order.
Lucy's (main area) - yummy homemade ice cream.
Others:
Pizzeria Leo in Chemyuil
Casa Cenote in Tankah Tres (Sunday's are an all-you-can-eat bbq)
Ana Y Jose's in Tulum
Que Fresco's (at Zama's) on the Tulum beach road towards Punta Allen
Al Cielo in Xpu Ha (beach club during the day, at night it's gourmet seafood on the beach)