The New York metropolitan area is served by LaGuardia (LGA), Kennedy (JFK), and Newark-Liberty (EWR) airports. The Port Authority of New York and New Jersey website has detailed pages for each airport that include sections on ground transportation options between the airports and Manhattan.
LaGuardia MTA Bus:
The only mass transit option between Manhattan and LaGuardia is the M60 Select Bus route (PDF) of the NYC Transit system. It travels back and forth between the airport terminals and the Morningside Heights neighborhood, including stops relatively close to GISS on Broadway at 116th St. and at 106th St. The M60 makes stops in Astoria, Queens, and in Harlem along the way. Although the bus schedule indicates the M60 should take 40 to 60 minutes to travel between the airport and GISS (depending on time of day), adverse traffic conditions can sometimes cause it to take as long as 90 minutes, most likely during weekday working hours or rush hour.
The airport bus stops are green-framed glass shelters located alongside the ground transport road just outside terminal baggage claim areas. The fare is $2.75 and must be paid in advance using one of the Select Bus Service kiosks adjacent to the shelters.
JFK AirTrain and Subway:
At JFK, the AirTrain monorail circulates around the various terminals and then leads off to the Howard Beach stop of the subway A train, to the Sutphin Blvd. stop of the subway E train, and to the Long Island Rail Road's Jamaica station. The AirTrain costs $5, and then you have to pay the subway ($2.75) or train fare ($7-$16) to get to Manhattan.
Depending on whether you connect with the A or the E, the AirTrain-plus-subway combo takes 50-80 minutes to get from the airport to Midtown Manhattan. The A is more convenient in traveling directly to GISS from the airport as you would only need to make one relatively easy transfer in Manhattan (at Columbus Circle), but is 20-30 minutes slower reaching Midtown than is the E (which requires a trickier transfer at Penn Station). The LIRR train from Jamaica station also connects to Penn Station in Manhattan.
Newark also has an AirTrain service that circulates around the terminals and connects with the Newark Liberty International Airport Train Station. From the airport station, you can take a New Jersey Transit or Amtrak train to New York Penn Station in Midtown Manhattan. (Note that you pass through Newark Penn Station on the way, so be careful that you do not exit the train at the wrong Penn station.) The AirTrain itself is free. NJT fare from the airport station into Manhattan is $15, which is much less than Amtrak charges. Travel time between EWR and New York Penn Station should take about 25 to 30 minutes, but is dependent on the NJT schedule and is subject to train delays.
Airport Shuttles, Van Service, and Taxis:
There are various airport van, shuttle and bus services that connect the airports to Manhattan. Some have set routes, typically with drop-off/pick-up locations in Midtown Manhattan locations such as Grand Central Terminal (Park Ave. at 42nd St.), Penn Station (Seventh Ave. at 33rd St.), and the Port Authority Bus Terminal (Eighth Ave. at 42nd St.). See the LGA, JFK, and EWR ground transportation webpages for more info and for links.
City taxi cabs operate between Manhattan and JFK or LaGuardia. However, NYC taxis may only deliver you to Newark, and only Newark cabs can bring you into Manhattan from the airport. When cabbing in from one of the airports, be sure to get a cab from the taxi stand outside the baggage claim area so that you will be charged the legally specified rate. Livery cab drivers who may be trying to pick up fares in the baggage claim areas may try to charge you more than a regular cabbie.
As of 2017, cab fare between Manhattan and LaGuardia (LGA) is around $30-$35, and there is a flat fare of $52 between Manhattan and JFK airport. The fare to/from Newark (EWR) is around $60, plus a $5 surcharge if you are coming from the airport or $17.50 if you are heading to the airport. Add to the fare about $5 for bridge/tunnel tolls as well as a tip. Thus, you can see that cab fare can be quite expensive, particularly to EWR. Using one of the alternative mass transit or airport bus services might be a bit slower and and less convenient but is significantly cheaper.
The NYC Taxi & Limousine Commission has more on their FAQ.
New York City is located on Amtrak's Northeast Corridor, on which the Acela offers fairly speedy travel to Boston, Philadelphia or Washington, D.C. Amtrak also offers service to Albany and upstate New York via the Empire Service. Trains stop at New York Penn Station in Midtown at Seventh Ave. and West 33rd St. Due to the lesser need to arrive at the station well in advance of departure time, travellers are likely to find that Amtrak is more convenient, more comfortable, and probably less expensive than air travel in serving the cities mentioned.
Commuter rail service is provided by the Metro-North Railroad, the Long Island Rail Road, and New Jersey Transit. Metro-North connects the city to communities on the Hudson River as far north as Poughkeepsie and in Connecticut as far east as New Haven, and terminates at Grand Central Terminal. Serving towns out on Long Island, the LIRR stops at Penn Station. NJT connects to various town in New Jersey and also operates out of Penn Station.