LOVE TO BE GOING NOW
we stayed in matagorda one year in lanzarote. where we stayed was lovely ( cnat remember name now ) your only about 5mins in taxi from the strip/clubs/bars/restaurants etc so can very easily go in at night but then your nicely away from it aswell if your looking for a nice chillaxing holiday without being in the hub bub of it all!! There was also a little shopping center/ out door place near us in matagorda that had lovely restaurants/bars aswell which was nice to go to one or two of the nights as you get tired of looking at the same thing on the strip.
so all in all id say they will love it as you get best of both worlds
Stayed there about 10 years ago in a hotel called the Bertiz Playa. Lovely hotel at the time but I don't know what its like now. Heard rumours thats its not as great as it use to be. Matagorda is lovely. Quite and not too far away from Puerto del Carmen, which has loads of bars, lovely resturants, nightclubs etc. Only about 3-4 euro in a taxi