We live in San Diego and if the weather is nice, you won't be the only ones on the beach;)
I suggest going downtown and visiting Seaport Village. After that, you can walk (or drive if it's too far for you) to the port and hop on a ferry to Coronado (inexpensive), then rent bikes and ride around Coronado and spend the day at the beach. If you visit the Hotel Del, you can go to their beach after viewing the Dr. Seuss sculpture garden exhibit. There is also usually a restaurant/bar patio playing music where you can grab a bite to eat and let the kids dance;) Also on the 23rd Coronado starts its Skating By The Sea where they create an outdoor ice rink overlooking the beach and a portion of the proceeds benefit Make A Wish Foundation.
Balboa Park has great activities (carousel), museums, etc. On November 19th, it is family day and is very inexpensive - check out this link for more information: http://www.balboapark.org/calendar/event/2011-11-19/famil....
Let's see what else do we locals do? We go to the park play area a lot at Balboa Park too - it's right behind the Science museum (that's another place we go as well).
Someone else mentioned The Children's Museum downtown and I concur, it's a great place to take kids. I think they have an exhibit right now called Trash that sounds really interesting and it may still be going on in November.
If you'll have a car and want to take a bit of a drive (about an hour), the annual Julian Fall Apple Days and Harvest will be going on through 11/30/11.
If you'll be in the La Jolla area, we like to take a day and go down to the children's pool (it's the beach) to let our son watch the seals. We first usually go to the La Jolla Recreation Center (walking distance to the pool) because they have an amazing playground - he has a great time using up his energy and then we have a picnic at the Children's Pool area. While there, you can also visit Birch Aquarium.
If you're staying downtown, but want to visit North County, you can hop on the Coaster (local train) to Encinitas or Solana Beach which both have a great little beach community and the train drops you off only blocks from the beach.
If your kids would be into it, the Old Globe Theater (inside Balboa Park) will start showing Dr. Seuss' How The Grinch Stole Christmas on 11/19/11 - but tickets go fast.
On 11/20/11, the annual Mother Goose Parade (free) will be going on. The Mother Goose Parade is the largest parade in San Diego County and the largest of its type west of the Mississippi. Each year, the parade attracts thousands of spectators to the streets of El Cajon, California to view the parade for free on the "Sunday before Thanksgiving." http://www.sandiego.org/event/Visitors/41
If your family likes to hike, there are many trails throughout San Diego County that are easily found online and aren't far from downtown San Diego.
Oh, and how could I forget, Yo Gabba Gabba Live will be in San Diego on 11/20/11. http://yogabbagabbalive.com/events/42-san-diego-civic-the....
Del Mar Fairgrounds: On the 24th, the Holiday of Lights starts at the Del Mar Fairgrounds. http://www.sandiego.org/event/Visitors/3133. The 25th through the 27th has the custom car & hot rods nationals going on.
Hope that helps. Have a great time!
-S.