Beacon is located on the MTA Metro North line and Amtrak transfers are available (Poughkeepsie), but is not very close to a major airport. Here are the main ways to get to town:

From NYC: Fly into Newark, JFK, or LaGuardia. Take local trains to Grand Central Station and then take the MTA Metro North Hudson line to Beacon. (From LaGuardia, you can catch this same Metro North train from the Harlem-125th Street station.)

From Albany: Albany is a smaller, quicker airport but requires a 2-hour drive down from the Capital Region.

The City of Beacon provides a free loop bus that runs around town, including the train station, art museum, and main street, about once every half hour.

https://destinationdutchess.com/listingsv/city-of-beacon-free-loop-bus

Main street is a pleasant 15-20 minute uphill walk from the train station and is the heart of Beacon. If you have a local AirBnB, you may be able to walk. Otherwise, there are typically a couple of local taxis at the train stations and 1-2 Ubers in town. (Beacon is pretty small, so don't plan on efficient Uber/Taxi service in off hours or out-of-the-way places.)

The bride and groom's family will also have a few cars available to shuttle small groups between event locations.