The Ghostbusters headquarters exterior is Hook & Ladder Company 8 at North Moore and Varick Streets in Tribeca, New York City. Wikipedia says the firehouse was built in 1903, still operates as an active fire station, and was used for exteriors only. Interiors were shot in Los Angeles.
Fans visit to see the full-size Ghostbusters sign above the main entrance, and Wikipedia reports an annual Ghostbusters Day celebration at the firehouse on the Saturday closest to June 8. Wikipedia describes no public tours.
Because it is a working station, never block the apparatus doors or the sidewalk in front, do not enter without permission, and move on quickly if a truck is leaving. More in our Halloween movie filming locations guide.