Looking for fun? The first place that comes to my mind are the classical Arenal and Magaluff, only 10km from Palma but they are really over crowded, I donīt recommend them, only if Uīre looking for bars and discos all day long. Other good place is Cala Blava. Itīs a nice place around 25km from palma, with nice not so crowded beaches and U have the city nearby. There are also Palma Nova, Portal Nous that could be other choices, about 15km from Palma. There are two other places, but in the other side of the island, Port Alcudia and Port Pollenca, with lot of bars and nigh clubs to choose from.
If looking for nice quiet places.... Port Andratx is a good place, 30km from Palma. It has some bars around where to have drinks and enjoy the sea breeze. Other good choice could be Sant Elm, is a very peacefull place, with a nice beach but is not so close to Palma, is about 40km and not so much night life. If U rent a car U will have many more options. Cala Millor, Cala Figuera, Cala Ratjada, Cala Murada, Cala Mallorca and may other places.
As U can see, there are many options, hope the info will be usefull.

