Taking advice from a person who's been a New Yorker for about two months? That's your first mistake.
Got a bridge I can sell you, wanna buy it?
From Grand Central Terminal (GCT) to JFK International Airport? There are several ways by public transportation, but if you go that route you'll need about an extra hour or two, depending on traffic. I'd just hail a cab at the taxi stand outside Grand Central on the corner of 42nd Street and Vanderbilt Avenue. Fastest way is by taxi.
To Columbia University (as in Columbia College, the Law School, the Business School, and anything OTHER THAN THE MEDICAL SCHOOL) from GCT you have to take the Shuttle or "S" train toward 42nd Street/Times Square and catch the Uptown Nos. 1 or 9 train and take that to 116th Street. For
Columbia College of Physicians & Surgeons/New York-Presbyterian Hospital Columbia Campus, take the Uptown No. 1 to 168th Street/Broadway.
To
New York University Medical Center/School of Medicine Medical Center from GCT take the Downtown No. 6 train from GCT to 33rd Street/Lexington Avenue and walk East to 1st Avenue. If you want NYU Washington Square (as in the Business School, the Law School, and the undergraduate colleges) take the Downtown No. 6 train to Astor Place/Cooper Union.
To
New York Medical College/Westchester Medical Center you'd take the Metro-North Railroad, stationed at Grand Central Terminal, to the Valhalla Station on the HARLEM line. Hail a cab.
To
Albert Einstein College of Medicine/Montefiore Medical Center take the Uptown/Bronx No. 5 train from GCT to East 180th Street and then the Morris Park Avenue/Bx 21 bus to Eastchester Road.
To
Mount Sinai School of Medicine take the Uptown/Bronx No. 6 train from GCT to East 96th Street/Lexington Avenue and walk West to Madison Avenue. Then walk North to 99th Street/Mount Sinai Hospital.
To
State University of New York Downstate Medical Center/College of Medicine take the Shuttle, "S" train, to Times Square/42nd Street to catch the Downtown/Brooklyn No. 2 train to Winthrop Street/Nostrand Avenue. Walk South on Nostrand Avenue to Clarkson Avenue and then walk East on Clarkson to the hospital (at the intersection with New York Avenue).
To
New York Institute of Technology/College of Osteopathic Medicine take the "S" train to Times Square/42nd Street to catch the Downtown/Brooklyn "A" or "C" or "E" trains to 34th Street/Pennsylvania Station. From Penn Station take the Oyster Bay line to Greenvale Station. Hail cab to NYIT/Old Westbury. It may be a little difficult to get a cab from Greenvale, so I'd take either the Port Jefferson, Babylon, or Ronkonkoma line to Hicksville Station and take a cab from there. The campus is on Route 25A/Northern Boulevard in Old Westbury, LI, near the Old Brookville campus of Long Island University.
To
University of Rochester School of Medicine and Dentistry/Strong Memorial Hospital -- you're in the WRONG town.
