Be careful what you ask for...
Here is my suggestion...
Dana Point Harbour. Lots of picnic groves with grills, tables and little shelters.
Dog friendly but they must be on leash. Tons of dogs all the time.
Easy access from I5.
Plentiful and clean restrooms.
Other activities - boat tours (whale watching, etc.) in the harbour. Beaches.
I suggest either October 12 or 19 (both Sundays.)
Not terribly expensive motel if needed. (Has been used by a couple of PetTalkers who can comment...)
Located between San Clemente and San Juan Capistrano.
http://www.danapointharbor.com/