When rolling Mr Monopoly do I move to Auction to a property
The latter (you move to the next property which has cheaper rent.). It's not the next "place" in the rule, it's the next property .

From The Rules


  If you roll a Mr. Monopoly after all of the properties are
  owned, make a normal move according to the white
  dice, then move ahead to the first property on which you
  need to pay rent


(emphasis added)