Despite being a group of islands that has officially changed hands numerous times throughout history, the Balearics have been able to retain some of the cooking that makes them distinct while also incorporating Spanish influences and opening its doors to assimilate modern international flavors. Islands like Mallorca and Menorca are not exempt from fast food chains known worldwide (you can't even walk into an indigenous village nowadays without seeing a billboard touting a quarter pound of beef and special sauce), but there are plenty of traditional restaurants, tapas bars, and other establishments worth a look.
Mallorca in particular is the cuisine capital of the islands. Here, you'll find an exceptional seafood paella (rice-based with vegetables) that rivals that found in Barcelona that will also be less expensive. The maroon Sobrasada is a paprika-spiced pork that is very popular in local dishes, while Ensaïmada is a typical breakfast pastry unique in that it is cooked with pork lard. The Frit Mallorquí is also an interesting dinner option, consisting of different animal parts (lungs, liver, etc.) cooked with local vegetables in Mallorcan olive oil.
When in Mallorca, Palma will undoubtedly provide the most options for eating out. There are plenty of good tapas restaurants around the city, particularly near its attractive public squares. The area around the Santa Catalina Market is pretty highly concentrated, while the market itself has a great variety of basic foods. Patrón Lunares is a trendy Spanish spot, while Joan Frau and the aptly named Diner are great for unpretentious dining in the neighborhood. There are also a ton of restaurants along the west end of the harbor along both Avinguda de Joan Miró and Avinguda de Gabriel Roca; there is a broader variety of food here, although much can be a bit more expensive with the view. There are an assortment of restaurants around the island, but two stand out at Mallorca's center: S'Hostal and Es Cruce. S'Hostal (on the outskirts of Montuïri) does a Mallorcan specialty called Pamboli with the best of them, while Es Cruce (in Vilafranca de Bonany) is a mecca for traditional dishes.
Menorca, the smaller and much less touristy of the two islands, has an adequate array of dining options, particularly in Mao and Ciutadella. The best part of Menorca is that in every small community with an ocean view there are always at least a handful of places that have terraces and good food with which to enjoy it. For example, Sa Gavina in Arenal d'en Castell (northeast Menorca) is known for its traditional Spanish dishes, friendly staff, and views of the ocean landscape. Another is Puig de Sa Roca, a largely unknown farmhouse at the foot of Monte Toro that also does stellar Menorcan dishes. Then again, the best way to find a decent restaurant is to take a stroll down their main street (usually running parallel to the beach) and pick a place that looks busy.
For more information on where to eat when visiting both Mallorca and Menorca, take a look through our included activity pages.