The following restaurants and bakeries are truly (and decidedly!) tree nut–free (and peanut-free, unless otherwise noted), and should therefore be safe for the nut-allergic. They generally take care to ensure there are no nuts or nut traces in their food—or, at the very least, they categorize themselves as nut-free.
(For a list of places that aren't declaredly "nut-free" but that don't knowingly have any nuts or nut products lying around, see this page.)
A La Mode Shoppe (360 E 55th St)
A nut-free ice cream parlor (and children's boutique) with gluten-free and dairy-free options, too.
Bagel Town (488 Hempstead Ave)
A nut-free, sesame-free, dairy-free kosher bagel shop on Long Island.
Baked Cravings (1673 Lexington Avenue)
A nut-free bakery that offers cupcakes, whoopie pies, brownies, and custom cakes.
BaZnGa CaFe (426 Amsterdam Avenue)
A science-themed café with a nut-free kitchen—and a kosher certification. (Do note, though, that while BaZnGa's owners have decided to market is as a nut-free restaurant, they don't require their vendors' facilities to be nut-free, which means that some items—like breads—may in fact contain trace amounts of nuts.)
Big Daddy's Restaurant (multiple locations)
A kitschy, old-timer American diner with a nut-free kitchen (though some items made off-site aren't guaranteed to be free from cross-contamination—and they use Frangelico, which is made with hazelnuts. See this post for more information).
Butterflake Bake Shop (448 Cedar Lane)
A nut-free kosher bakery in Teaneck, NJ.
Cakes 'N Shapes (466 W 51st St)
Custom nut-free cakes and cookies.
Cerbone's Bakery (140 S Ridge St)
A nut-free kosher bakery in Rye Brook, NY.
The Donut Pub (203 W 14th St)
24/7 donuts, bagels, sandwiches, muffins, cookies, scones, biscuits, cakes, and, of course, coffee. (Bonus: they do croissant donuts!)
Duke's Original Roadhouse (multiple locations)
A Southern-style sports bar that shares its ownership with Big Daddy's (and that likely has similar caveats).
Everybody Eats, Inc. (294 3rd Ave)
A nut-free, gluten-free bakery in Brooklyn. It's more office than storefront, but they do sell breads, bagels, cakes, pastas, etc.
Heisler Pastry (1321 North Ave)
A nut-free kosher bakery in New Rochelle, NY.
The Little Daisy Bake Shop (622 Valley Road)
A nut-free bakery in Montclair, NJ.
Sofia's Creations (no storefront)
Custom cakes, cupcakes, cake pops.
Sofia Pizza Shoppe (989 1st Avenue)
Pizzas and rolls made in a nut-free kitchen.
Zuckerbakers (2845 Jerusalem Ave)
A Long Island kosher bakery that's entirely free from nuts, dairy, and sesame.