Many possibilities!

You can go out in Nerja, Malaga and Granada. The last two are located one hour away.
Nerja is a little smaller, but equally enjoyable.

Nerja has a vibrant nightlife in the summer months of late night bars, pubs and clubs that stay open until the wee hours. In high season there is plenty to do. Start with a tour at some of the local tapas bars who offer a delicious variety of traditional Spanish tapas: steamed mussels, spicy shrimp, local cheeses and "chorizo​​" sausage.
El Chispa in Calle San Pedro has a good reputation for a varied selection of tasty tapas.

Restaurants
Local specialties include many fish and you'll find some great fish restaurants. Try red pepper with fish and shellfish, "migas' breadcrumbs with garlic and clams, sea bream and red mullet from local waters, fish broth and noodles or the famous Andalusian" pescaito frito "fried fish.
There are good Italian, Chinese and other international restaurants, along with the inevitable burger bars and fish and chips.

Bars and clubs
El Molino Bar is one of the most typical flamenco bars in Nerja. It is probably the oldest bar in Nerja. Every night there is live music.

Most of the nightlife is centered around Antonio Millon and the adjacent square Tutti Frutti. This area is dotted with bars, many with music and live entertainment, they come to life around midnight and it takes until the early morning in high season.
Nightclubs: Jimmy at Antonio Millón, Castillo at Diputación Narixa , you can find it in an alley on the seaward side of the church on the Balcon de Europa.

Málaga en Granada
Information about nightlife in Malaga can be found here Going out in Málaga
General information about Malaga can be found here City info

Information about nightlife in Granada can be found here Going out in Granada
General information about Granada can be found here City info