As with so many destinations in the Mediterranean, the answer to the eternal question of "what to eat" is, honestly, anything. After all, the cuisine of this entire region is known for its freshness and originality, and Mallorca is no exception.
As Chopin noted over a century and a half ago, it is a place ripe with agriculture. You will find groves of all kinds, but the proximity to the sea means that even the mountaintop locations have the ability to offer you today's freshest catches.
However, if you want to be absolutely sure you have sampled what a local Mallorcan would call their specialties, be sure you taste "sobrassada" which is a very spicy pork sausage found in a diversity of dishes as well as served on its own with some bread and vegetables. Another must is "ensaimada" which is the ideal holiday breakfast food. Shaped like a spiral, and created in Mallorca, it is made from a basic dough that uses pork lard but which results in a sweet pastry. The prevalence of almond trees on the island results in a lot of dishes that use it as a main ingredient, and you will often find ice creams as well as cakes made from them. Of course, paella of many kinds is found throughout Spain, but Mallorca's twist on this dish is to make it mostly of seafood rather than a blend of meats. If you are hoping for a true Mallorcan meal, book a table at a "celler", which is a defunct wine cellar converted into a restaurant. Here you will enjoy true specialties of the island, with two of the best spots noted being Sineu and Inca.
Remember too that Mallorca is Spanish, so the meals are later than in many other locales. Lunch begins at 1PM and can run past 3PM while dinners rarely begin before 8PM and can take up to two hours to complete. Coffee after your meal is always a short shot of espresso, and brandy or cognac is a preferred after dinner beverage. The island is also noted for its herbal liqueurs.