Even though I've sailed my own boat in the waters around San Diego, I've also chartered there a couple of times some years ago. Once leaving Harbor Island of San Diego Bay (SDB) on a Catalina 25 (Marina Sailing) and one other time leaving Quiveria Basin of Mission Bay on a Capri 22 (Seaforth), I believe. I've also used Marina Sailing sailing out of Long Beach and Oxnard, CA, and was once a member of Marina Sailing in Long Beach. It's a good company. They appear to have larger boats available in SDB than those mentioned above at Seaforth. The Cat 25 we took out some distance past Pt. Loma and then back. The Capri 22 we sailed up into "Sail Bay" inside Mission Bay. Both venues have something to offer, but there is much more stuff to see from the water starting in San Diego Bay. However, if you wish to go into the ocean and sail along the coast, leaving from Mission Bay using Seaforth (if they let you go outside) would likely be the better choice.
One caveat--going out the channel at Mission Bay can be a challenge if the wind and sea are up from the west or southwest; it's likely to be a "motor-boater" (wind on the nose) experience where you may need to wait to hoist the mainsail until
after clearing the channel. The kids might be sick in the first 30 min just getting out there if the sea/swell is up and they are not "sailors." Staying inside Mission Bay is fine, but it's only a couple of hours worth of sailing, IMHO. If you go outside in Santa Ana conditions stay near the coast. Those winds are from the east and northeast, and can be quite strong and gusty.
https://marinasailing.com/Harbors/Harbors/HarborInfo?HarborCode=SD