Granada, Malaga, Ronda, Cordoba, and Antequera
Granada is, of course, world-famous for its Alhambra, and if you have never been there before, a visit really is a must! From Los dos Algarrobos Granada is easily reached with a day trip. We recommend reserving tickets in advance: save yourself queueing at the entrance and be assured of a time slot for visiting the Palacios Nazaries (royal chambers).
Also, Malaga is a great town, hosting the Picasso museum. Otherwise, Malaga is a very cosy, Spanish harbour town with accompanying cathedral, parks, markets, and bodegas where you can drink the famous Malaga wine directly from the barrel. Furthermore, Malaga is a wonderful shopping opportunity.
Other cities you can visit in a day are Ronda, Cordoba, and Antequera.
Velez-Malaga, Torre del Mar, Nerja, Almuñecar, and Salobreña
A little closer, there a few smaller towns: Velez-Malaga (the regional capital, very Spanish), Torre del Mar, and Nerja. Nerja is a bustling town with an old Moorish centre: a labyrinth of narrow, pedestrian-only streets, housing restaurants, shops and tapas bars. Where once was a 10th century fortress, there is now the Balcon de Europa, offering a fantastic view of the sea and the coast line.
Further East, you'll find two more interesting towns: Almuñecar and Salobreña. Both are rooted in Moorish tradition, which shows. They are very Spanish towns, definitely worth a visit.