Regarding players cards, it's a bit difficult to explain ... but I'll try.
The Casinos in Los Angeles county have live games and poker, but no slots, no craps, no roulette.
Some of the clubs still have players cards though.
The Indian (Native American) casinos do have slot machines and all, or nearly all, have slot card programs.
However, there aren't any Indian Casinos in Los Angeles county at all. The nearest are in San Diego or Riverside or San Bernadino Counties.
A minimum of 1 hour each way from the LA Airport, and they are pretty spread out, except for a grouping in northern San Diego county.
Best bet is to start with this Wikipedia list, and sort on the "County" column. Look for casinos in Los Angeles County. Plus, if you want to drive more, also look at San Diego, Riverside and San Bernadino counties too.
Then check websites of each one you may want to hit to see if they have a players card program AND if you want to drive to it. Personally, it's not how I would spend a vacation. Not like the Las Vegas experience of going up & down the Strip to get lots of cards. It will be an effort!
Having said that, the nearest casinos to LAX airport would be those in Gardena, CA (several of them), then the Bicycle Casino and the Commerce Casino (south of downtown LA).
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