Any of the restaurants in Santa Catalina are good and the area is good for breakfast, lunch, or dinner. Hostal Cuba is lovely for a glass of wine, tapas and people-watching and they also have a roof terrace. Wasabi is a good Japanese and there are a couple of ok Italian restaurants on the pedestrian street. Mr Xiao, Koh, Vandal, Duke, Sumaq, and Market Kitchen are all popular with locals as well.
Mana Taco in town is a good Mexican, and La Rosa Vermuteria nearby has great tapas.
Bar at the top of Hotel Almudaina for drinks, not a meal.
Mercat Olivar for lunch.
It is lovely to sit in La Lonja in the evening, but some of the tapas bars in the old town are a bit old-fashioned and pricy. La Boveda used to be ok, Merchants if you want to splash out. Winings across from merchants used to be ok. Bar Dia is a bit of an establishment.
Plaza Raymundo on the other side of town is nice and all of the restaurants are good. Placa De La Quartera is a nice square nearby as well.
Portixol and Molinar areas nearby have great restaurants and little bars and there is a beach.
Palma itself has a big beach.
Cala Mayor is a nearby beach, but it gets quite busy.
Illetas or Portals beaches are also easy on the bus if you don't have a car