* Nothing is greater than finding a huge park to wear down the kids. In Monterey, that is Dennis the Menace Park. It is open daily from 10am to dusk. A map is here, which includes directions. More detailed information about this park and pictures are listed here. There is limited parking right in front of the park, but when that fills up you have to drive around a little to find something nearby.
* Rent a paddle boat at Lake El Estero, next to the park. Rentals are by the half-hour or by the hour. You can chase ducks if your legs are quick enough, or simply mosey around a small island in the middle of the lake. You may find some folks fishing from the lake, as it is stocked. Its also a nice place if you are a bird watcher. There is a skateboard park nearby and around the lake are exercise stations.
Restaurants immediately close to the park are McDonalds and a liquor / wine store that has a deli inside. If you are looking to picnic at the park, these may be your best bet. Sit-down restaurants can be found at the wharf nearby.