Flight
NYC airports are a 1.5 hour drive up to CT. (Excluding Newark which will take about 2.5 hours). Hartford/Springfield airport (Bradley) is about a 45 minute drive to the wedding.
Train
From NYC you can take amtrak directly to Old Saybrook. The cheaper alternative is to take metro north from Grand Central or Harlem to New Haven and then change to Shoreline east which will make stops along the shoreline (including guilford, branford and old saybrook).
Hotel
Hotel
Hotel
Hotel
If you're planning on taking Metro North from NYC, you may consider staying in New Haven. It's an easy ride from Grand Central. New Haven is a 20 min uber ride to Guilford (The local Shoreline east rail also goes into Guilford, CT)