The best places tend to be on the calle Carabeo. Beware! They´re expensive! At the bottom are the Parador villas which are near the Parador hotel (hence the name). These are 3 to 5 bed villas with private pools.
https://www.holidaynerja.co.uk/nerja/rentals/LUR049.htm#.XPn8e4-xW1s
http://www.hotelcarabeo.com/boutique_hotels_nerja/boutique_hotels_nerja_self_catering.asp
https://www.holidaynerja.co.uk/nerja/rentals/LUR042.htm#.XPn7n4-xW1s
https://www.holidaynerja.co.uk/nerja/rentals/LUR040.htm#.XPn8Io-xW1s
https://www.holidaynerja.co.uk/nerja/rentals/LUR041.htm#.XPn8Q4-xW1s
https://www.holidaynerja.co.uk/nerja/rentals/CVI2.htm#.XPn7vY-xW1s
https://www.holidaynerja.co.uk/nerja/rentals/CVI3.htm#.XPn72Y-xW1s
https://www.holidaynerja.co.uk/nerja/rentals/LUR044.htm#.XPn7U4-xW1s
https://www.holidaynerja.co.uk/nerja/rentals/CVI1.htm#.XPn8C4-xW1s
https://www.holidaynerja.co.uk/parador_villas_nerja.htm