Carmel-by-the-Sea
Beaches - Hit the beaches but don't expect to swim - the water in Carmel Bay is cold, and even in July, it can be overcast. Still, some of the most beautiful scenery in the world is along this coast, so make time for a picnic or a stroll along one of the beaches here. The most kid friendly beach is Carmel Beach (at the foot of Ocean Ave.), bring your beach toys and build sand castles all afternoon. One of the least crowded is Carmel River State Beach, where the Carmel River runs into the ocean and the dunes serve as perfect "lounge chairs."
Parks - Carmel Beach City Park, right at the bottom of Carmel Hill is a great place to enjoy a sandwich. Forrest Hill Park near Junipero and Camino del Monte is also home to the Forest Theatre, where sitting under the spreading oak trees will transport you to a mythic place. Mission Trail Park near Rio Road just south of town is a great spot to pause while on a trek from town to the Mission.
Mission San Carlos Borromeo de Carmelo is one of the most beautiful of all the California missions. Take time to explore the gardens (don't miss the small graveyard with markers dating back to the mid 1700s) and the interior exhibits of mission life (including a padre's cell, refectory, library). This is a working church as well, with baptisms and weddings and prayers, so children should be reminded to enter the church itself with respect. It's an easy walk from Ocean Ave down Mission Street to the mission.
Point Lobos - From Carmel it's just a short drive to Point Lobos State Reserve (go early in the day to get parking).
Fun food
A favorite thing to do as a kid (and even now, with my own kids) is to get a sandwich and picnic on the stone benches in Devendorf Plaza in town. Bruno's Market has a deli counter where they'll make you a tasty (and huge) sandwich any way you like it.