Van Nuys, Burbank, Whiteman, or Santa Monica. Check AvWeb or AOPA FBO listings and then phone them for particular information. The Valley (VNY, WHP, BUR) will clear stratus earlier (if it's an issue when you want to fly) than SMO. Airspace is not all that formidable especially now with GPS, and approaching from the north for the Valley means you're only dealing with Class C. If you do fly between SMO and VNY/BUR, be real careful about staying in the window below LAX Class B and the top of BUR Class C. It's 200 feet tall, and the only really tight part of the airspace. If you approach from the south as a TX'n might, just fly up the coast and through the SFR corridor over LAX. Don't need to talk to anyone. The LAX terminal chart is your best friend; making it your homework assignment will get you comfortable.
There are plenty of perfectly adequate and not-hard-to-access GA airports throughout the basin, but you'll starve to death in traffic jams. I find driving far more stressful than flying the basin. Maybe because I lived there for 50 years.
John Siebold