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You might wish to read The Points Guy blog (thepointsguy.com if I remember). He had a post just this week (I think it was June 30, 2011) on American Airlines awards.
LAX is an AA gateway city, so stopovers are allowed in LAX on an award ticket. If I understand the AA rules correctly, once you have enough AA miles for an award ticket, you could have a stopoff at LAX and then later continue on to take a vacation in Hawaii.