A few years ago we stayed in a pretty town up the coast from Malaga, called La Herrudura, visited many places along that coastline such as Mijas, Nerja and Frigiliana, all lovely very majestic outlooks, in Mijas, great al fresco dining with fantastic views. A day at The Alhambra, Granada is an absolute must it's such an amazing place, worth the drive if you are interested in history. I haven't spent any time in Malaga itself, I imagine it's quite interesting being part of old Al Andulacia . On separate trips to Spain, we went to Ronda, an interesting town reached by a very twisty, mountainous road, we had our travel sick son with us at the time and kept having to stop, didn't realise just how many hair pin bends there would be on the way before we set off. I love the Moorish part of Spain, particularly Seville and Cordoba.
Hope you enjoy your trip OP, such a great country for culture. food, language. May and June I imagine it's pretty hot down in southern Spain.