From Newark Airport: It is quite easy to get to Robert Treat Hotel from the Newark International Airport.
The hotel provides free shuttle services to and from the airport. One can take a taxi to the hotel for $11.00.
There are also bus services from the airport to the Penn Station in Newark (note that there is also a Penn Station in New York City). Then you can take a cab or take the city subway to Military Park (one stop). Then it is a short walk to the hotel (50 Park Pl).
Still another option is take the AirTrain monorail from the airport to the airport train station. Then take any NJ train in the direction of New York one stop to Newark Penn Station and proceed as above. For more information, see here.
If you arrive at the JFK airport or the LaGuardia Airport, then you can take the subway or shuttle to the Penn Station in New York City (note that there is also a Penn Station in Newark). From there you take one of the New Jersey Transit trains (one stop) to the Penn Station in Newark. Then you can take a cab or the city subway as described in the last paragraph.