The Forbes article New York Architects Plan Enormous Skyscraper Hanging From An Asteroid In Space describes a sky scraper suspended from an asteroid in a geosynchronous (but not geostationary) orbit that does not quite touch the Earth. The orbit is inclined with respect to the Earth's equator, and slightly elliptical. This is the recipe for a figure-eight ground track, and several answers here describe them in more detail (I'll try to find links to a few, if you know a good one, please add it.)
Question: Because the orbit is elliptical, will it only approach the Earth's surface for "boarding" at periapsis in the southern hemisphere, or could you enter this building when it was over New York City as well?
note 1: As pointed out nicely by @sweber, the path shown can not be the ground track of a compact object in orbit. It goes up to about 41 North in latitude but only down to about 18 South. But the building is something more like a a 2D pendulum with Coriolis(?), so need to look closer at what the plot represents.
note 2: Remember that the earth is oblate by many kilometers!
below: All images are from the Clouds AO website for the Analemma Tower concept, first one is cropped from the second one.
below: from Google Street View - anyone who doesn't believe that things from space touch down in NYC hasn't been there, or at least hasn't seen MIB.