Flight
LaGuardia Airport (LGA): This airport is East of Manhattan, and Montauk is a 2 hour & 15 minute drive from here John F. Kennedy Airport (JFK): This airport is East of Manhattan, and Montauk is a 2 hour & 15 minute drive from here MacArthur Airport (ISP): This is a Long Island airport, and Montauk is a 1.5 hour drive from here Newark Airport (EWR): This is a New Jersey airport, West of Manhattan, and Montauk is a 2.5 hour drive from here
Travel Note
All of the airports we recommended above have major car rental companies. If you are traveling into an airport we highly recommend factoring in a rental car with your transportation. You can also check the Turo App, which sometimes has cheaper rental car options than the major car rental companies!
Train
If you can't or don't want to rent a car, you can take the Long Island Rail Road (LIRR). This is a cheaper, but lengthier travel option. It will be easiest to take the LIRR from JFK or LGA. From each of these airports, you will need to get to Jamaica station, and then get off there and connect to the LIRR train towards Montauk. You can then expect a 3.5-4 hour train ride from there. If you are spending time in NYC before the wedding, you can take the LIRR from Penn Staton to Montauk (you will need to switch trains at Ronkonkoma). This is roughly a 3 hour & 15 minute train ride. Website with train schedule information below: http://www.mta.info/schedules
Travel Note
One other cost effective option if you will be spending some time in New York City before heading to Montauk is the Hampton Jitney. This is a shuttle service, and will likely be the most cost effective option, but will also take around 4 hours. Website below: Hampton Jitney: https://www.hamptonjitney.com/hjmobile/ **Once in Montauk Uber operates and there are also multiple Taxi companies, so getting around there is easy**