Regarding the Ecto Goggles:
It might be advisable to leave them at home, as well as any of the more technical-looking elements of the belts, you don’t want airport security mistaking them for something more malevolent… and as there are restrictions on real Night Vision Goggles, the people working security might mistaken them for the real deal.
As for the locations, there used to be a pretty good film location website… but it went belly-up a few years back.
Ghostbusters
The Firehouse: Corner of N.Moore Street and Varrick.
-Take the 1 train to Franklin Street Station, exit the station and walk one block north and you should see the Firehouse.
55 Central Park West/Columbus Circle/Tavern on the Green
-Take the 1 train from Franklin to Columbus Circle Station. Disembark for the Circle (where Stay Puft appears) and then walk six blocks north for Dana’s apartment building. Tavern on the Green is located almost directly opposite 55 Central Park West.
Columbia University
-Take the 1 train to the 116th Street Station. “Weaver Hall” was in fact the Schermerhorn Hall building on the campus, located at the north-eastern corner. Ray and Peter’s conversation on the steps after they’ve been kicked out take place on a raised section next to the CV Star East Asian Library building, overlooking the main square of the campus in front of The Graduate School of Arts and Sciences.
City Hall/“The Loading Dock”
-Take the 4, 5 or 6 to City Hall - Brooklyn Bridge Station, there should be an entrance on the edge of City Hall Park. You will be able to see City Hall from a distance, but since at least 2001 there has been a tight control of who can and can’t get close to City Hall. The “loading dock” was actually filmed at the Municipal Building (identifiable by the golden statue on the top).
New York Public Library/The Bank
-Take the 7 train to the 42nd Street – Bryant Park / Fifth Avenue station, there should be signage directing you to the Library if there isn’t a stop nearby, but sticking to Fifth Avenue should result in you finding it quickly. The bank exterior (although substantially changed) is located across the street from the Library, to the left of “Superfund”.
Lincoln Center
-Take the 1 train to 66th Street - Lincoln Center Station and walk one block south, or walk east and one block south from 55 Central Park West.
Rockefeller Center
- Take the B, D, M or F trains to the 47th–50th Streets – Rockefeller Center Station, walk one block north and then one block east to reach the area featuring the skating rink/statue of Prometheus.
Ghostbusters II
The Courthouse
- Walk one block north from the Municipal Building into Foley Square, the Courthouse is located on the south-eastern side of the square.
Peter’s Apartment: Corner of Broadway and Bleecker Street
-Take the 6 train to Bleecker Street Station and walk one block west or the B, D, F or M trains to Broadway-Lafayette Station and walk half a block west and one block North.
Dana’s Apartment/First Avenue Dig: 325 East 77th Street
-Take the 4 or 6 trains to 77th Street Station, and walk two and a half blocks East for the filming exterior of Dana’s Apartment. Walk the rest of the block to the intersection with First Avenue where the baby carriage rolled out into traffic(this is not the same location where the dig was filmed - that happened in Los Angeles).
The Museum: U.S. Customs House
-Take the 4 or 5 trains to Bowling Green Station, it should be visible from the street entrance.
The Statue of Liberty
-Take the 1 train to South Ferry Station and board one of the Circle Line boats to Liberty Island (if you wish to enter the statue, be sure to book your tickets in advance online to avoid disappointment)
Washington Square Arch
-Take the A, B, C, D, E, F or M trains to West 4th Street Station and walk one block east.
There are more locations scattered through the two movies, but those are the main ones.
For more info, here’s Scouting NY's two-part feature on the first movie’s filming locations:
Scouting NY: Ghostbusters - Part 1
Scouting NY: Ghostbusters - Part 2
Additional location
Van Horne Station
If you fancy seeing one of the real-world inspirations for the disused, slime-filled train station in the second movie, stay on the 6 train as it leaves City Hall - Brooklyn Bridge Station to head back uptown… you should be treated with a brief view of the “ghost” City Hall station, closed since 1945: City Hall (IRT Lexington Avenue Line)