Ditto on the rental car. LA is VERY spread out and taxis are horrifically expensive. Just the round-trip taxi fare between LAX and Long Beach could easily pay for a day's car rental.
As far as accomodations, I also agree with Mossman in that LAX is a good base for your explorations. There are many hotels nearby of all price ranges. When near LAX, try to stay west of I-405 (San Diego Freeway) otherwise you'll end up in a rather questionable area. Anaheim, in "The O.C." is another area with a large concentration of hotels (due to Disneyland) but is not real convenient to most of LA's tourist traps and dive destinations. Hollywood, West Hollywood, Beverly Hills, and the eastern San Fernando Valley (Studio City, Burbank, Glendale) are more convenient to the tourist traps but you'll have a long drive to the shoreline and airport. Long Beach has some hotels but parts of that city are quite questionable, I would definitely inquire here about any potential lodging there before making non-refundable deposits. There's nothing wrong with staying at any of the downtown LA luxury hotels, except you'll be bored to tears. There's little to see in the daytime and the place is a ghost town at night.
Local laws -- the only ones I can think of is that if shore diving off Laguna Beach (in "The O.C."), a snorkel and a dive buddy are required. Other than that there's nothing you need to be concerned about, especially if using a charter operation. Dive charters usually assign "insta-buddies" if you didn't bring your own. Keep in mind though that unlike warm water dive destinations, our charter boats offer little more than mere transportation to/from the dive site and air fills. Some don't even offer food.
For the limited time you'll be here, San Diego may be a bit too far as you'll be on the road for 2 hours each way, longer is traffic is bad (and it might be that weekend as Monday is Presidents' Day). If you really want to see San Diego, seriously consider taking Amtrak as it's cheap and is just as fast as by car, faster if traffic's bad. Only thing is that you'll need to make your way to downtown (Union Station) or else one of the train stations in northern Orange County to catch it. However, there is an inexpensive shuttle service called the "Union Station FlyAway" which picks you up at LAX and drops you off at Union Station if you're considering doing this.
however I arrive at LAX on the 17 February and should be through by 20;00 I haven't booked ant accomodation or diving. I have read about the Kelp but other than that I don't know anyhing about the diving. 
