Here are some of my top picks for using points and miles to get to Cancun and how to make the most of a trip there with your credit card benefits. And by redeeming Alaska Airlines Atmos Rewards points for American Airlines flights instead of AA's own miles, you can sometimes save a ton. AMERICAN AIRLINESCompare that to the 9,000-22,000 miles American Airlines would charge you in economy, or the astounding sum of 20,000-59,500 miles in first class plus taxes and fees of around $62. Avoid resort fees when redeeming hotel points in CancunOne of the biggest scourges when it comes to booking beach vacations these days is resort fees. For instance, the JW Marriott Cancun Resort & Spa charges a relatively modest resort fee of $35 per room, per day.