Just as a clarification, SOTs are not the same as recreational class boats. Recreational class boats are limited in the conditions that they should be taken in due to lack of inherent flotation should they flip. SOTs have inherent flotation and can be appropriate for some pretty big conditions. Almost as extreme conditions as sea kayaks (assuming paddler has skill to match what boat can do).
The sea kayak gets its ability to handle more extreme conditions through using a skirt. SOTs don’t have any gear needed to make them work in conditions. So a sea kayak without a skirt is a boat that should be kept to much mellower conditions than a SOT.
But a sea kayak without a skirt, assuming you know how to self rescue in it (and have any tools you may need, like paddle float), could be used in more extreme conditions than a recreational class kayak.
Bringing this back to SoCal, if you use your boat without skirts and assuming you have knowledge and kit needed to do self rescues, I would stick to places where you are not launching on a beach. If conditions are mellow, you could paddle out a harbor into open ocean or the like. But beaches on ocean are pretty universally going to have surf that you need to launch through. Without a skirt, even a mellow surf will be working on flooding your boat.
La Jolla Cove is a great paddle. Lots of leopard sharks off the beach. Sea lions and garibaldi over by the rocks. But it is a surf launch. I second the suggestion of just renting a SOT that day to get to experience that. Even in boats not as good as yours, it would be a fun experience.
San Diego could be interesting to paddle San Diego Bay or Mission Bay.
In OC, outside of doing surfing there isn’t that much that excites me for paddling.
If you are doing just 1 or 2 paddles during a longer trip, you could rent sea kayaks at Aqua Adventures in Mission Bay. That would save the hassle of carrying your own. That said, most rentals of sea kayaks with skirts are going to require that you have taken a class that had you successfully do a paddlefloat rescue, which you haven’t said if you’ve done or not.
Or consider doing the SoCal thing and renting SUPs or AquaBikes or some other vessel totally different at one place or another…
Reference - here is the American Canoe Association’s info (as translated by Roger Schumann and printed in this book: https://amzn.to/3jT1blb) description of different flat water categories and what vessel is appropriate to use in them:
A sea kayak without skirt they would say would be good for L1 or L2. A SOT can go to L4.