It's amazing how many library systems we have in San Diego County. Where we live, there are library branches from at least 3 library systems within 15 minutes. Every library system offers free events for kids.
San Diego County Libraries
The San Diego County Library system has nearly 3 dozen locations serving San Diego County from Jacumba to Fallbrook. Chances are there is a County library near you. Their events calendar is online here.
San Diego City Libraries
The San Diego City Library system also has around 3 dozen locations, from San Ysidro up to Rancho Bernardo. Their events calendar is online here.
Escondido Library
The Escondido Library only has one location now, unless they reopen the East Valley Branch. They have a lot of children's events, both ongoing and non-recurring events. Their calendar is here.
Carlsbad Library
The Carlsbad Library has two locations. They have a lot of ongoing events at both branches. Their children's programs are listed here.
Oceanside Library
The Oceanside Library has two locations. I have not used this library system, but they do have a lot of children's events listed here.