Book your reservation at the Mirage directly through the Mirage website. This makes you automatically eligible for Priority room upgrade status. If the hotel is fairly busy though, an upgrade may take a little extra effort.
Mention a special occasion when you check in and be polite with the front desk person. If you say you are having a birthday, anniversary, bachelor or bachelorette weekend or a wedding and are extra friendly with the person checking you in, they might upgrade you just because they want to.
Fold a $20 bill in between your drivers license and your credit card when you hand it over to the front desk clerk. If he/she asks what it is for, tell him/her that you would love to get an upgrade if possible.