Bluefin tuna generally are around off southern California in mid-summer (July through September), though they seldom show as far north as L.A., except way offshore (like the Cortez Bank, which is 100 miles out). You'll do better out of San Diego -- those charter boats can run south into Mexican waters, where the tuna are generally much more numerous, and depending on the conditions (water temperature, time of year, etc.) you can catch bluefin, yellowfin, or albacore tuna. In late summer the L.A. area boats can sometimes get into the tuna, but generally they have to run south to get them unless the water is warmer than usual that year.
There's no closed season for tuna -- it's just that they need warmer water, and when it cools in the fall and winter, they just leave this part of the ocean for warmer parts.
Main San Diego sportfishing landings:
http://www.fishermanslanding.com/
http://www.hmlanding.com/
http://www.pointlomasportfishing.com/ | 
When is a good time to fish in Southern California? 
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