Hi, Julian -
(Sorry for the delay - I tried to reply last week but was having trouble logging in...)
Gina is right on about May. In general, IMO, March through May are not ideal in California. Springtime = storms and upwellings, so although we sometimes get great nudibranchs and jellies...they are often in mucky, green water. We dove Catalina a week ago, and although we found pockets of decent vis, it was not great by any stretch of the imagination, maybe 40 ft max at one site; I heard that wreck alley had 10 ft vis max on the same weekend. We also dove twice in La Jolla over the past week, but San Diego's been experiencing a south swell, so we've had weird currents and less than optimal visibility.
San Clemente Island is consistently good and can range to incredible, but the biggest issue this time of year is the crossing - you need calm seas. If it's iffy, you can cross to find yourself trapped in one lame anchorage for the whole trip.
The oil rigs are one of my favorite So Cal sites, but I try to avoid diving them between February and about July simply because I can - I've experienced worse visibility and current in the spring than any other time of year - the rigs are daunting on a good day, and on a 15 ft vis day with a 1+ kt current and/or lots of surge, it is tough to see what the fuss is about.
In short - while the weather/vis here is always hit or miss, if you can plan a trip for August through October, you're giving yourself the best chance to get a great day.
For San Diego, we love Waterhorse Charters for the wrecks/day trips.
For San Clemente, if you can do a multiday, Horizon out of San Diego is a nice boat; if you're farther north, check the Sundiver (out of San Pedro) schedule to see if they are running to SC and/or Santa Barbara.
For the oil rigs, Catalina (including Farnsworth), and even day trips to San Clemente, we use Selky Charters (out of Huntington Beach). This is a six pack operation with no compressor on board, and you'll have to prearrange any gear needs (including tanks/weights), but the captain will tailor to your wants/needs - book ahead, as she is in demand. The Sea Bass (out of San Pedro) also runs rigs and Catalina day trips, and they have a compressor on board (EANx was being fixed last time we were on, but he should have it running by now).
Hope this helps you plan future visits - California is incredible, even with the hit-or-miss nature - keep coming back, it is worth it! Hope you enjoy Point Lobos - what an incredible site.