The only public transportation in Groton are yellow school buses. But you have options: 1) Rent a car. 2) Take the commuter rail (the Fitchburg Line) from North Station in Boston to either the Ayer Station or the Littleton/495 Station (depending on which hotel you choose). Then carpool with friends from there.
The Marriott and Hilton share an eleven passenger van. They've graciously offered to shuttle some guests to/from the hotel and the reception (not the church). If you're interested, there will be a sign up sheet when you check in.
During the champagne toast, ask a server for non-alcoholic cider instead (adults). The bar will have soft drink options for kids and adults.
The Marriott SpringHill Suites encourages guests to party in the lobby (to keep noise out of the bedrooms). Matt and Rebecca will be off towards their honeymoon, but we encourage you to continue reconnecting with old friends if the spirit moves you. It's BYOB and BYOsnacks (nothing in Groton or Ayer is open at that hour).