Would not recommend TJ for a family trip. For one thing it's not a very family orientated town to vacation in the first place, for another the cartels have made a considerable push into the area over the past 5-6 years. If you just want to take your family down to Baja Mexico, then I recommend towns further south of the border. Rosarita is just to the south of Tijuana, but nowhere near as trashy. Ensenada, is a little farther south and has some very cool whale watching spots.
I lived in the San Diego area for 2 years and loved my time there. Downtown has plenty of tourist street shopping and restaurants to see. A short walk from there to the pier and you can take your family on board the USS Midway. Balboa park is a neat area, close to the San Diego zoo, which the family will enjoy. After you're done in Sea World, there are a few other amusement park areas close to the Mission Beach area, Belmont Park is right down the road, and I believe LegoLand is close by, but might be more closer towards Carlsbad. Anaheim and LA is also a short 1.5-2 hour drive up the road on I-5. You can find a lot to do up there as well (Universal Studios/Disneyland/Knott's Berry Farm/ etc.).