I would second the recommendation for La Bamba Jarocha. I especially like their mixed seafood soup.
I would also say that, come hell or high water, you need to make it to HC. Its my favorite restaurant in Playa, and one of my favorites in the world.
I'm a fan of the seafood at El Cejas. Large selection of fresh seafood (including several types of ceviche), well prepared with pride.
You may also want to try La Borrega across from the McDonald's on 307 for authentic central Mexico barbacoa.
All of these places will give you excellent, authentic local food at a good value.
I agree with the suggestions about Negro Sol, but its not really "local" nor is it inexpensive. But good food and good service. I had a GREAT date there a couple of months ago with THREE lovely ladies, NONE OF WHICH WERE MY WIFE!!! (Did I mention how much I love Playa?
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