Mayorships are based on the most *days* with check-ins in the past 60 days (you could have more check-ins overall but fewer check-ins over the past 60 days). Keep in mind that you might find yourself neck and neck with another user who is checking in to the venue often, in which case that's all part of the fun!
In order to be eligible, the setting "Participate in foursquare Mayorships" must be checked and you must have a profile photo. You can upload a photo to your account on the app or at http://foursquare.com/settings. Click on "edit" next to Account Info. **Photos must be 200 KB or smaller (jpg, gif, or png format).
Make sure you aren't checking in privately ("off the grid"). Off the grid check-ins do not count towards the Mayorship tally and will not unlock a Mayorship. When you check in, make sure to select Yes to "Share with friends?" and you should be able to unlock a crown. Only users who have legit check-ins (no rapid-fire check-ins, no drive-by check-ins, and no fake check-ins) will be able to reign.
Oh, and if you’re using the mobile website at m.foursquare.com, your check-ins will not count towards the Mayor tally. Details here.