There are several family friendly resorts in and around Runaway Bay ranging in size from 3 to 300 rooms. The type of vacation you're looking for will decide in many ways which is best suited to your family.
Starfish Trelawny in Falmouth is the largest (for now) and the oldest and most popular in the area, and other popular ones include
Royal Decameron Club Caribbean,
FDR, and
FDR Pebbles which are all significantly smaller. They are presently building a 1200 room Barcelo Resort just west of the Runaway Bay area. Another great family option is the
Silver Sands Villas property.