Traveling to The Reunion

Amtrak is the passenger railroad which has regular trains between Boston, Providence, and New York. In Boston, you can go right from the train to the subway, which they call "The T". Same with New York. The subways can take you to and from the airports.

You can check out Amtrak schedules and see how late they are on their website. Most Amtrak trains use Penn Station in New York City. The station code is NYP. If you want to get to the "T" in Boston, go to South Station, downtown (code BOS). The train station in Providence (code PVD) is just south of the state Capitol, which is within walking distance of downtown.

Amtrak has trains all over the USA, of course, but they are a bad way to get around unless you have lots of time. And they generally run very late. 

The Boston airport, Logan, is the closest large airport to Rhode Island.  From there it will take you a couple hours, by car or train/subway, to Providence.
The Rhode Island airport is small and has mainly regional planes.

New York City has 3 airports: LaGuardia, Kennedy and Newark (which is actually in New Jersey). Kennedy is a little closer to Rhode Island.

Going to and from Detroit, we like to go through Canada at Port Huron. It will take you 11 hours plus stops. Rochester, NY is about the midpoint. Rome isn't.