You should rent a villa or an apartment with a pool. There are plenty of options - all of them listed online in sites like airbnb, homeaway and even on hotel sites like booking.com. Alternately, if you like the comfort of a hotel, Hotel Carabeo comes recommended.
If you have a car, you could stay at Malaga and then drive down to Nerja or base yourself in Las Alpujarras, a cluster of white villages spread around the southern Sierra Nevada.The latter is for those who prefer solitude and serenity and happen to visit Costa Del Sol in high season.
In terms of best area to stay at Nerja, my choice is Carabeo area. The area is flat and all the restaurants are at an easy walking distance. You can also look at Torrecilla which is on the western side and nearer to the beaches.
Another option I’d recommend is the Verano Azul apartments. A bit further away from town but still within walking distance. Centrally located between the beaches and balcony of Europe. In terms of apartments, you will also find many options on Calle Malaga.