Benidorm used to be the best place to take the kids. It has beaches, amusement arcades, water parks, theme parks and animal parks.
In autumn 2008 a new bylaw was passed which makes digging in the sand on the beach (even kids sand castles), or playing ball games on the beach punishable with a fine of over 170 euros. This has spoilt the location as a destination for a low cost day out.
Try the beaches at Villa Joyosa 12kms from Benidorm, or around Alicante instead. You will not have so many off sand amusements for the kids, but you will avoid a big fuine should your child make a hole in the sand.