There are lots of quaint, little shops in the old town. Look for streets calle Pintada, Almirante Ferrandis and Carabeo.
Market day is Tuesday from 8.30am to 1.30pm. They also have a flea market at the same spot and time on Sundays. See map link.
https://goo.gl/maps/aTNNovVN41Et3qWn9
The main nightclub area is known as Plaza Tutti Frutti (this has 8 bars and nightclubs that open from 10pm till 6am!)
There are lots of things to do in Nerja. Golf, kayaking, snorkelling, scuba diving, boat trips, pedaloes, visit the famous caves or just sunbathing, eating and drinking!