Here are some ideas:

Visit the Caves of Nerja - A large underground cave complex with stalactites and stalagmites

Hiking in the mountains around, Nerja. - There are hundreds of interesting hiking trails around Nerja with excellent views.

Going to the beach in Nerja. - Nerja has a small beach.

A stroll along the Balcón de Europa. - This is a long promenade looking out to see.

A trip to Frigiliana. A very attractive whitewashed village just inland from Nerja.

Maro beach. ...

Nerja has a good Indian restaurant which is not very common in Spain.

Visit the little village of  Acebuchal. Needs a car. There are two good restaurants.

For a list of paid (not free) activities, excursions, trips etc 

Click here There are plenty of day trips and other things to do.