I lived in SB for nearly 20 years. These were among my favorite spots, but I have not been in a few years. I was a poor grad student or dived with poor students, so most of our activities were beach diving.
Refugio has a great reef that runs from the point on the west side of the park and extends east. I must have hundreds of dives on that reef. Yes, there is oil but it is usually not too bad. It is an easy kick to the edge of the reef. One the east side of the park there is a series of undercut ledges. Kelp usually marks the edges of the reef, but given the high surf events this winter I am not sure how much is there.
Another spot is Hendry's Beach (Arroyo Burro County Park) at the junction of Los Positas and and Cliff Drive. Easy parking (if you can find a spot) and an easy entry. Reef is off to the west.
East of Hendry's is Mowhawk Reef accessible from a set of 240 steps down to the beach. Parking was in the neighborhood at the top of the stairs but the locals can get a little territorial if they think you are surfing. Cliff Drive to the light at Mesa Lane takes you to the spot.
Finally, one of my favorite spots is the the 6800 block of Del Playa in Isla Vista. There should be access to the beach. The kelp is thick, and in about 25 feet of water it is a lobster haven. Save enough air to swim back in under the kelp and dive it at high tide. It is one of the more tarry spots around.
If there is a high surf event or a rainstorm don't bother to get into the water at any of these places, the mudline will be quite visible and water quality will suck.