Pefkos in Rhodes? Nice long beach. I stayed there when the kids were young in the Matina Appts which were 1 min from the beach so not too busy round the pool. The rest of the resort is up a hill but there are restaurants/minimarkets within a 2 min walk. It's 1.5 hr transfer (less than 1hr in a taxi) and 5-10 mins taxi ride from Lindos with its Acropolis,
Chania and the area around it in Western Crete is lovely. It will get hot in July/August high summer but not oppressively so on the coast. The villages around Chania have gently sloping shallow water and it's nice to visit Chania itself, with its Venetian harbour/old town, covered markets and fantastic bakeries (walnut baklava to die for).
The further west you go the more remote it is, but there is definitely tourist infrastructure even in the remote places, and some of the most amazing beaches are there (Falasarna, Elafonisi lagoon etc).
Loutro/Finix on the south west coast which is really lovely but quite quiet and old fashioned, and accessible only by a coach across the island and then a boat along the coast so if you don't want a long transfer that is maybe not for you...Paleochora is a bit bigger and more of an established resort, and it usually does have a breeze (people windsurf there).
Cretan food is simple and delicious and it's a great place with kids.
We haven't been since the crisis but we are going back this year, have missed it too much.
I like Pefkos. DH and I stayed at the Island Blue hotel, but you could still self cater if you wanted to. They have a sister hotel close by called the Pefki Islands which is cheaper, but you still get a small kitchenette and a bedroom off the main bedroom which is handy for kids. You can use all the pools and facilities of both. I think a lot of the hotels are actually 'apart-hotels' which gives the flexibility to families, and you can still eat out. Lots of lovely restaurants to choose from.
Google Pefkos and you will find a lot of reviews, maps, pictures and holiday companies to help you decide.