Dedicate a couple days of your trip to checking out Catalina Island. Take a ferry across and spend the night. Dive the Casino Point Underwater Park. It's very accessible shore diving. You can rent equipment there and hire a local DM, if you like.
It's certainly possible to travel across by ferry to Catalina, do a couple of dives, and then return to the mainland, but it makes for a really long day.
If you only have one day, it might be better just to do some dives off of a dive boat that leaves from/returns to the mainland. Non-divers in your travel party can amuse themselves in LA doing any number of things.