Hola,
if your choices are to fly to Malaga or Alicante, both have nice places where you can drive to.
A general impression is that near Alicante is less built up than Malaga - I havnt stayed in Alicante itself, but in some small resorts to the north - Denia and Javea. They are pretty places, and the drive there between the mountains and coast is lovely. Its mainly spanish tourists which go there too.
Near Malaga there is certainly lots to do. You could stay in quieter town on the beach like Nerja or Torre del Mar if you didnt want to be in the thick of Malaga. Lots of day trip possibilities - e.g. to Ronda, Granada, Marbella.
As Dr M said, the Costa de la Luz is fab - deserted huge long beaches, authentic feel to the towns, not bult up atall, but getting there is a long drive from Malaga.
Maybe read up in a Rough Guide, to get more info on the places..