All you have to do to earn the foursquare navigator badge is like the Smithsonian National Air & Space Museum on foursquare and then check-in to the museum. You will then earn your shiny new badge and see the following message:
Congrats, Navigator! Did you use a sextant or GPS to find your way here? Now, navigate over to the “Time and Navigation” exhibition inside the Air and Space Museum to hone your skills.
Enjoy the new exhibit!