One word for me - brunch. NY is the world capital at Brunch and there are some amazing places to go for it, including Blue Ribbon Bakery, Bubby's, Cafe Mogador, Florent and Barney Greengrass the Sturgeon King.
Go to the Grand Central Station Oyster Bar and Katz's Deli - both great and iconic.
The best show I saw on Broadway was Cabaret at Studio 54. It's great if it's still on, as they made the venue into a Berlin style supper/cabaret club with waitress service and amazing cocktails.
The bar at the Tribeca Grand is a good spot for a cocktail and people watching.
East Village is great for vintage and funky shops.
Jeffrey's Department Store, near the Meatpacking District, is fab. It has the most amazing shoe department ever.
Museums are great - MOMA, the Met and the Guggenheim.
All the other stuff you've planned sounds great.