I've always liked Punta Sal as a quiet and relaxing alternative to Mancora. I'm not sure how the new Decamaron has affected the area, as I haven't been up that way since it opened. Punta Sal has got a nice sandy beach, it's relatively quiet and beautiful. The only drawback was a lack of good places to eat - there are a few which are okayish - but you can always take a taxi or a moto to Mancora.
By the way, if you do stay in Mancora, Las Pocitas is generally very quiet and family friendly with some great hotels. So you have the advantage of being close to the centre of Mancora with all its restaurants and bars without having to be around the party crowd when you go to bed, or if you just want to relax on a quiet sandy beach during the day with your children. I can PM you a few choices if you do decide to go there. Although the beach is nice and clean, the drawback here is that the sea is a little rocky, so it can be a little difficult if you like to swim. But for children, there are lots of little pools and places to play.
Los Organos, as Teamoperu says, is a good choice. It's very quiet and the beach is very sandy and there aren't as many rocks in the sea as in Mancora. Although my personal experience was a little negative. For some reason there was a lot of litter on the beach and a couple of dead sea lions, which put me off going for a swim. I also found it windier than Mancora and Punta Sal, although I don't know if this is because it has a more exposed location, or if it was just windy that day, but it seemed a great choice if you like paragliding or wind surfing.