You didnt mention a budget so, in my opinion, its the Hotel Riu Palace Maspalomas -rates very highly on Tripadvisor - but comes out about £110 a night in September.
http://www.riu.com/en/
Many thanks for the reply. The Riu Palace Maspalomas is at the Playa del Ingles end of the dunes where there seem to be fewer facilities than at the Meloneras end where there is a shopping centre and lots of restaurants. As far as I can see, at the Faro/Meloneras end, most of the hotels seem to be 5* which is probably what we would go for to treat ourselves. Just wondering if anybody has first hand experience.
Just returned from Cordial Mogan Playa in Mogan, not cheap but lovely hotel although eat out in the evening. Four minute easy mainly flat walk to harbour and lots of restaurants. Child friendly hotel, enjoyed it. Friday market literally on doorstep.