Papi's Cuban & Caribbean Grill 4349 Lawrenceville Hwy Ste E, Tucker, GA30084 Papi's Cuban & Caribbean Grill is an award-winning restaurant specializing in authentic Cuban and Caribbean cuisine.…More It has five locations throughout the Atlanta area. Papi's brings indigenous tropical flavors prepared by expert chefs using fresh ingredients. The menu features sandwiches, wraps, entrees, burgers, soups and salads, vegetarian items and homemade desserts. The restaurant has a full bar and serves tropical drinks and cocktails, and hosts live salsa music. It is open for eating in, take-out and catering.