Things to do on Sunday for (mostly) free
Broadway on Broadway - the casts from 20+ Broadway shows will be performing live on Broadway between 43d and 47th, starting at 11:30. Michael McKean (Spinal Tap, an upcoming play) is hosting.
Brooklyn Book Festival - Readings, panels, authors, performances. celebrity guests (including Pete Hamill, Oliver Sacks, Edwige Danticat, Tom Tomorrow, Leonard Lopate, and Melvin van Peebles) and new this year, a day of Comic Con events
Harbor Day - Free events on the waterfront (part of the NY400 festivities)
on the Battery - Royalty on bikes and yacht spotting
Battery Park City - Harmony on the Hudson (live entertainment, including Tom Chapin and the Double Dutch Divas)
Hudson River Park - Oysters, boat races and the Half Moon
Governor's Island - Free performances (and some you buy tickets for), dutch food, free ferry rides to the island (the last boat leaves at midnight)
Brooklyn - Biking in Breukelen has free bike rentals, extreme BMX demonstrations, bike riding lessons (bring your own bike), "bike smoothies" and a flea market
Staten Island - Dutch art, furniture and films at the Snug Harbor Cultural Center. Also, beer.
Other waterfront activities: free kayaking in Manhattan and Queens, a County Fair and a concert in Riverside Park, and walking tours of Fort Tryon Park
a Petanque Tournament in Bryant Park
29th Annual Motorcycle Show at the Queens County Farm Museum (probably one of the very few motorcycle shows with a petting zoo). Admission charged.
Harvest Day - The kids can make cider and apple fritters and help pick and cook the potato crop. Lefferts House, Prospect Park
Romeo and Juliet - from the Curious Frog Theater Company, in Prospect Park
1864-rules baseball - 3 teams, 3 games, Washington Park in Brooklyn
Get a head start on your leaf peeping with walking tours of the Brooklyn Botanic Gardens and the Central Park Ramble
Red Hook Jazz Festival (organizers say to bring blankets to sit on)
Queens County Folk Festival - world music and jazz at Queens College
American Musical Theater Concert in Verdi Square (Upper West Side)
Jazz in the Park in Weeping Beach Park, Queens
Harp and flute (and crafts for the kids) at Dyckman House (Washington Heights)