Teddy Roosevelts House! https://www.nps.gov/sahi/index.htm Teddy's grave and Audubon Society; tombstones and birds! https://ny.audubon.org/trsac
Cute little historic downtown, with a brewery https://oysterbaybrewing.com/ The best Italian Ices ever, still family run, fresh ingredients. I recommend the mango, strawberry, and lemon! https://www.bonanzasitalianices.com Check out the beach and play ground! https://oysterbaytown.com/departments/parks/parks/ Feel free to explore and enjoy the grounds of the Planting Fields Arboretum where the wedding ceremony will take place. https://plantingfields.org/
This Gold Coast era mansion has a Natural History Museum and Planetarium!! A little farther into Long Island, but a lovely day can be spent there.
Check out this calm rocky beach with views of Connecticut. There are plenty of cute bars and restaurants', with a kids adventure park. https://www.longislandpress.com/2019/05/09/bayville-a-waterfront-north-shore-best-kept-secret/ Walls Wharf has a very cute beach bar and brunch. https://www.wallswharf.com/