At present, Foursquare only has additional privacy controls for places categorized as 'Home.'
To make sure your home on Foursquare is private to you and your friends (and that only you and your Foursquare friends are able to earn the mayorship), choose Home as the place’s primary category. Doing this will ensure that only you and your friends can see the address on the place page; everyone else sees a zoomed out map with no map pin (rather than the real location). If a mayorship, badge unlock, or check-in is shared to Twitter or Facebook, the place URL will include a map without a specific location for everyone.
Only you and those you've added as friends on Foursquare will be able to earn the Mayorship of your home.
Delete your home
If you created the venue for your home and you categorized it as “Home,” you'll have the option to edit or delete it! Go to its venue page at Foursquare.com, log in to your account, and click "Edit Venue” under the map. Click the little trash can icon to permanently remove the venue from Foursquare.
If you did not create the venue for your home and would like us to remove it, please go to the venue page on the website and click “Report a Problem” for a list of flagging options. Select “Venue is my home” and click “I want to remove my home from Foursquare.” If you have more information, enter it into the space provided. Then click “Submit” to complete your request! We’ll look into it as soon as we can.