Recently tried some new places in Playa and just wanted to put a word in for two that are notable.
For your sweet tooth, La Casa del Chocolate, is an amazing cafe where you can get homemade Belgian chocolates and cakes/pastries. The owner is Belgian and makes incredibly delicious (so delicious, it feels sinful eating one of his creations!) chocolate cakes - my favorite is the chocolate mousse with pear. Light and melts in your mouth. They also make baguettes for 30 pesos so it's a nice light lunch place, too. Location: 4th St. between 5th and 10th Avenues.
For meat-lovers, try the Grillmeister on 10th St. between 10th and 15th Avenues. Here you can get tasty handmade German sausages for a very reasonable price, as well as home-made sauerkraut. Where else in Playa can one find that?! If you want to grill at home, can also buy sausages to take with you. There are other offerings on the menu, but this is definitely a place for carnivores!