A little farther north is Disneyland and Knott's Berry Farm.
A bit more north of that is Los Angeles, with lots of museums, some free. Getty Center for art! There's also the Getty Villa that's more family oriented also. For the kids, the Science Center (Space Shuttle Endeavor is here) and La Brea Tar Pits are good picks.
I agree with most of the recommendations above with some caveats. Depends what you want your vacation to be about and whether you want to rent a car. I wouldn't go to Dana Point (1 hour drive) to watch whales when you could just go to Dana Landing in SD and catch a boat to go whale watching. Disney, Universal, and Knotts Berry farm are about 1.5 hours. Disney is Disney and great. Next door is California Adventures. Also cool. Universal has many rides and characters that the kids may know.Transformers, Jurassic Park, Minions, etc. I don't like to spend my holidays driving too much, but your milage may vary.
Birch aquarium is in La Jolla, but Sea World may have enough to satisfy the kids. Sea World is near the beach so the weather will be more moderate than inland. For animals, the Zoo in Balboa Park is world class. They are open late in the summer. I say that because it is possible to go early when the animals are more lively, then go to the beach (or somewhere) mid day, and come back at night when it is cooler again. The zoo is huge with many hills and blacktop paths. Hot in the summer. The Wild Animal park is about 45 minutes northeast. It will be 10-20 degrees hotter than the beach. If you are at the zoo in Balboa Park, you might want to go to the Museum of modern history. Full of dinosaurs, saber-toothed tigers, sharks, fossils, rocks, etc. Down the hill towards the harbor is the USS Midway. It is open for tours and some summer nights they play movies on the deck.
A fun option is to take the ferry from the B street pier over to Coronado Island. You can drive if you prefer. You can rent bikes at the ferry landing. I usually ride south around the SD bay and over to the Hotel del Coronado and back to have BBQ at Miss Piggy's at the ferry landing. They have a great beach at Coronado island. Sundays in summer, they have free concerts at the pavilion on Orange Ave.
Consider Belmont Park at the beach in Mission Beach (SD). They have little rides and games for kids. A zip line, climbing wall, roller coaster. It's at the beach with plenty of places to eat and drink nearby.
I like to ride my bike on the boardwalk. It goes around the bay and the ocean front. You can rent a bike anywhere. You might consider either early or later when the boardwalk is not so congested. Bayside is always calmer than the beach side. In Mission bay, you can rent power or sail boats, paddle boards, etc on El Carmel point. Or the Catamaran hotel rents sail boats and bikes. Good place for a drink if the riding or the kids make you thirsty. The kids would enjoy a beach bonfire. The fire has to be in a fire ring. Claim yours early. Another option is people who will bring the fire pit, and wood to you and clean it up afterwards. The Catamaran shows movies on the sand (bayside) some summer night for free. Kate Sessions park has free concerts in summer.
As far as beaches and kids: I recommend certain locations where there are bathrooms nearby. Parking can be challenging if you get there late. In south Mission, there is a parking lot and new bathrooms. At the foot of Grand, there are bathrooms and food nearby. At the foot of Diamond there are bathrooms and a staircase down to the beach. At the foot of Law street there are bathrooms. At any of these locations, walk north or south as far as you want but near the restrooms. Swimming is in a different location from surfing for obvious reasons. Make sure you are where you want to be. Surf lessons could be fun. On the bluff at the foot of Law street, there is donation based yoga Sat/Sun at 10 am. Beautiful location overlooking the ocean. I think Steve also does it on Tues/Thursday but I don't know the times. You can search for yoga by Steve if interested.
The kids might enjoy the hang glider port in La Jolla. It is near the university. Turn on Salk Institute (polio). You can arrange a tandem ride if you or your kids wants a thrill. South of that is La Jolla Shores. A nice beach. South of that is the Cove. Good diving, but terrible parking. The drive along Coast boulevard from there is pretty. Many sea lions and seals sunning on the rocks from the cove south.
The possibilities are endless. This will be a good start. Enjoy your visit.