What a thoughtful birthday present!
In July 2011, LAX was about a 40-minute car ride to the Harbor Blvd. area so it's the farthest out of the three airports (we stayed at Homewood Suites). This was during non-rush hours. Not a super-long drive, but there are closer and smaller airports out there. I flew American, which was in a completely separate terminal from the rest of LAX. It felt like a long shuttle ride just to get to baggage claim. The Delta terminal was right next door, so I walked there in no time to meet my family. But other than that, you could be facing a long walk if you are meeting others (I'm sure there is shuttle that can drop you off at the other terminals). It sounds like it's just you and your wife for this trip, so this probably doesn't apply to you.
Your post indicated that you don't have to check into LAX on the flight home, which is great for you! I found LAX check-in to be a little stressful and lengthy and personally would love to avoid it for future DLR trips if I can find affordable, nonstop flights elsewhere. Some of it was American's fault. Plus, the TSA agent honestly started stuff with my sister and me (same agent, two separate incidents)--and we are not the types to stir trouble!
I'm used to flying in and out of chaotic, massive airports (including JFK, LaGuardia and Newark) and found LAX to be on par or worse than Newark.
With all of the above being said, I will always choose a nonstop flight ANYWHERE and ANYTIME over one with connections, primarily because you're flying during winter. I hope that this does NOT happen, but I'd hate for you to have a layover in the middle of nowhere just because you chose a closer airport and then get delayed due to inclement weather. This happened to me one December when I flew to Las Vegas from New York with a stop in St. Louis (I chose a flight with a connection to save money). It was one of the biggest blizzards the country had seen. I never made it to Vegas.

Because it was weather-related and "beyond their control," American did nothing to compensate for the trouble.
And a note about the car rental at LAX because someone mentioned it. I did not personally rent the car but was at National when my family returned theirs. Drop-off took seconds, but you do have to take a shuttle that goes to all the terminals before you get to yours.
If it saves you lots of money and miles, which it sounds like it, definitely fly into LAX and build extra time into your schedule (just in case).