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.