Whether you're going under cover or just want a bit more privacy, here's How To Turn Off Your Location on Facebook.
Feel like you're sharing a little too much? Maintain a little mystery in your life, or perhaps cover your tracks, by turning off your account's location settings. These settings on your Facebook profile automatically add a general location to all of your posts.
Turning off location settings from the Facebook app:
The fastest and easiest way to keep a location from appearing in status updates or chats is to go into your phone's privacy settings and turn off the location services. The location services use GPS and crowd-sourced Wi-Fi to triangulate your approximate location. Many different applications use the location services—Twitter has a similar setting where you can stamp tweets with an approximate location, too. By turning this setting off, you're not allowing Facebook to access this information.
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Be sure to only turn off location services for the Facebook app rather than your entire device if you're still intending to use location-specific apps like Google Maps, Find My iPhone, or the weather app.
If you've got Facebook location services enabled or have previously checked into a location, you may see your current city at the bottom left of the field when updating your status on the Facebook app.
To delete this, tap the pin icon. A list of nearby check-ins will appear. Tap the "x" next to the current city at the bottom of the list, and your location will magically disappear.
This will also stop Facebook from automatically including a location in your subsequent posts. If you change your mind and decide to reveal your location to the world, you'll have to manually enter your location by tapping the same pin icon and typing in your whereabouts. The setting will continue to stay "on" until you turn it off as before.
Want to keep information about your whereabouts more exclusive? You can also refine who can see your location by selecting the audience in a dropdown box.
Turning off location settings from a computer:
Same thing goes as the mobile version. Facebook will automatically suggest a general location for your post. To get rid of it, click the pin icon and hit "x" to remove the location and post ever so covertly.
Some apps and games also access your location information. According to Facebook, you can click the cog button in the upper-right corner of any Facebook page and select Account settings. From there, click apps and look for the setting Apps others use and click Edit Settings. Then uncheck the box next to "My status updates" and you're all sorted.
For parents concerned about kids over-sharing on social media, Facebook says it automatically shuts off location sharing for minors. And should the location setting be turned on by an account held by a minor, Facebook says it offers a consistent indicator the user is sharing his or her location.