Actually, there are a couple of popular overnight anchorages in San Diego area. First is Glorietta Bay in Coronado Island. The second would be Mariner's Cove in Mission Bay... and the other is La Playa near the Southwestern Yacht Club on Shelter Island in San Diego Bay...(weekends only).
Now.... the big challenge is to find a charter company that will allow you to keep the boat out overnight... I don't think Seaforth is set up that way..not sure, but I would be pleasantly surprised if they were. There's a Seaforth facility near me in Mission Bay. All types of rentals, sport fishing, restaurant.. etc. Easy enough to google them and check out what they have.
One trip suggestion..... Sailing from Mission Bay all the way down to Chula Vista, renting a slip overnight in their excellent marina, partying at the local restaurant, then trekking back the next day to MB is one option that I have experienced.... ocean and bay sailing plus some motoring... about 25-30 miles travel... each way.