This long strip is the center of town and full of great options for shopping and dining. Walking distance from the Delamar and Greenwich Harbor. The Delamar hotel also provides a free shuttle to and from Greenwich Avenue.
This is a fantastic public 18-hole golf course that generally books up quickly on summer weekends. Would definitely recommend booking in advance to be safe. This course is a ~15 minute drive from downtown.
Also walking distance from the Delamar Hotel and Greenwich Avenue, this is a beautiful park with tennis courts and plenty of space to walk/picnic.
The Bruce Museum is a stone's throw from the Delamar Hotel and hosts a wide range of art/history exhibitions. It was also just completed a multi-year renovation last winter and is worth stopping by for a coffee just to see the architecture/campus.
Island Beach is an incredible public island that is accessible via a ~5-10 minute ferry ride that picks up right next to the Delamar Hotel. The tickets are unfortunately only available for purchase online from Monday-Friday 9a-1p at the attached link but I would highly recommend buying ahead of time as it is a great way to spend the day.
The listed phone number is for the Delamar's experience manager who can coordinate a boat rental for small groups. You can take the boat around the Long Island Sound and (hopefully) catch some sun before the ceremony begins.