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Flight
There are a number of airports that will get you close to Connecticut. Westchester (HPN) is the closest, but has more limited flight options. JFK, Laguardia (LGA) and Newark (EWR) are all about an hour and a half drive to reach your destination. Newark has its own Amtrak stop and you could take a train to complete the rest of your trip. If you get from JFK or Laguardia to Grand Central or Penn Station you can take a train from NY to CT as well.
Train
The closest Amtrak stop is Stamford, CT. The northeast regional has regular trains running there from DC, NY, Philly, and Boston.
Train
If traveling from NYC you can take a metro north train from Grand Central to a number of Connecticut towns. South Norwalk is a hub that will have the most train options. Westport has its own stop, but East Norwalk, Southport or Fairfield may be closer to where you are staying depending on the hotel.
Travel Note
3 hours from Boston 1 hour from NYC 2.5 hours from Philadelphia 3 hours from Wilkes Barre, PA 5 hours from Washington, DC