LAX is convenient to nothing other than LAX*, but if you don’t mind taking 20 minutes to get anywhere, and over an hour to get to either destination it is sort of centrally located for those two spots.
The problem is that Irvine and Beverly Hills are roughly 70 miles away from each other with some of the worst traffic in the city separating them. Trying to stay centralized by staying at LAX would be roughly equivalent to deciding that you wanted to visit both Philadelphia and Manhattan, so you stay in Trenton, New Jersey**. Yeah, it’s sort of central, but it isn’t really close to where you want to be.
On any given day it WILL take you over 45 minutes to get from LAX to Beverly Hills, it will take you over an hour to get to Hollywood. If you don’t mind the driving and you want to let your wife do the tourist thing, stay in Santa Monica or Century City. Both have some very nice hotels and are closer to the tourist areas. Santa Monica makes a good tourist area in and of itself. Century City doesn’t but is very close to several. Both are close to the 405 freeway so you can get down to Orange County relatively quickly. This makes them better choices than Hollywood or West Hollywood which are farther from the freeways you need to get to Irvine. Culver City wouldn’t be a horrible choice either, but I am not sure what the hotel situation is like.
Downtown Long Beach has gotten very nice recently, but suffers from the same problem of inconvenience as LAX. It will take you an hour to get anywhere that isn’t Long Beach that is worth seeing. Also Long Beach is huge and some areas are very much not safe still.
Fullerton is a nice bedroom community, but there isn’t anything touristy there, same with Anaheim unless you plan on going to Disneyland, and it doesn’t sound like that’s the plan. All of Orange County makes for poor tourism IMO.
The other questions are, how is your wife planing on getting around? Will you each have your own car or do you plan to trade off with the car? What else does she want to see other than movie star homes? Are you interested in doing any touristy things yourself? Are you planning on doing anything together? How important is her ability to sight see vs. your ability to see old clients?
*Not strictly true, but close enough unless you want to spend time in El Segundo, Manhattan Beach, Hawthorn or Inglewood. And there there isn’t really much to do in any of those places as a tourist.
**Philly and Manhattan are a bit further apart, but not a whole lot. I am sure you get the general idea. The above example is a bit of an exaggeration since LAX is about 20 miles closer to Beverly Hills than Philadelphia is to Trenton, but it really is the absolute *worst *traffic in the city driving between the two. I want to put the distances involved into some sort of perspective.