Annie, I live near to Nerja but don't tend to go to bars and restaurants there so can't help with anything specific. There are loads to choose from though, around the Balcon are and also along Burriana Beach so I'm sure they won't have any difficulty in finding somewhere.
One that I've never been to but does have a conistently good reputation is 34 Carabeo on Calle Carabeo. I believe it is one of the more expensive ones though.
If your parents pop into one of the many estate agents, they will be able to pick up some of the free magazines, Ie Soltalk, Market Place, Streetwise. These have lots of advertisements and a browse through these might give your parents an idea of which reataurants to look out for.
Hope they have a great time.

For a really nice meal & a brilliant atmosphere, tell them to visit the Cafe del Mar down on Burriana Beach. It's run by a British couple (2 blokes), the food is fantastic & the service is brilliant. They may need to book a table the day before they want to go because it's very popular - i'm sure they'd really enjoy it.