Restaurants in the Balearics tend to cater for the Majorcan holiday maker, so you'll have no problem finding standard British, French and Italian fare.
Try a meal of Spanish tapas, a selection of small dishes such as olives, albondigas (meat or fish balls) and gambas al ajillo (garlic prawns).
Spanish rice dishes like paella are popular, and the seafood is mostly excellent, with grilled sardines being a local favourite.
In Palma, check out the area by Placa de Santa Eulalia, and between Placa de la Reina and the port for a good selection of restaurants.
For Palma's best eateries, try the maze of streets between Placa de la Reina and the port. Carrer dels Apuntadors is lined with restaurants and the Abaco - a crazy bar with crazily high prices.
Bar Martin in Carrer de la Santa Creu is cheaper and authentic, or the Cellar Sa Premsa for a hearty, cheap meal.
All the resorts have their own "scene" varying from the supremely (and superbly) tacky to the fairly tacky - which can, of course, be very enjoyable after a few beers and a long day on the beach.