Serious Eats - seriouseats.com

Levain bakery YES! The most amazing cookies ever!
And Baked - also a YES! But a shlep, this is true. But don't miss Levain, seriously.

Jacques Torres, hands down.
The treats at Pure Food and Wine's juice outpost, One Lucky Duck, and Babycakes NYC are worth checking out, even if you don't have food allergies and/or are raw or vegan.
The Petrossian on 7th has amazing treats, as does Cafe Lalo on the UWS, bakery or not.
Baked in Red Hook.
And DO NOT leave without trying the chocolate chip walnut cakes from Levain Bakery. They are a MUST.

Are you going to tell us where you ended up going? Serious Eaters' minds want to know!

Sweet Freak's list is awesome, I must say. I'll add, some from the Serious Eats link mentioned, that Two Red Hens in the UES and Black Hound in the EV are good. I haven't been to Bouchon yet, but my damn brother has probably spent $100 there in the past month (and he doesn't share!), and raves about them. They're pricey, but the oatmeal cookies and the triple chocolate eclair/pastry are two of his faves, so I've heard. If you were in the area more than a day, I'd say you MUST go to Baked; the entire menu is insane. But Red Hook is a hike/expensive cab ride or ferry trip.

But I fully agree with some of the Sweet Freak recs:
Chikalicious is yummy (for cupcakes and other treats), Sugar Sweet Sunshine makes a killer lemon cupcake, and I've heard great things of Butter Lane.
Momofuku's cookies (compost!!! and the corn flake one) are delicious, so are the cakes.
I've heard amazing things about Bespoke, and of course, Jacques Torres.
And Doughnut Plant's fried carby deliciousness is so worth the trip.

OK...let's cut the BS and get right down to it - Veniero's for cannoli, and anything else you want, but you have to have the cannoli!

Also, make sure to have a black & white cookie!

Amy's Bread actually has multiple locations as Ed pointed out on his Top 10 Bakeries in NYC list. I also like their cashew bars which run out very quickly.

Also, you may want to track down The Treats Truck. I'm a fan of their cranberry almond rice krispy bars and the butterscotch bars.

Thank you everyone for your terrific suggestions! Trying not to eat a large breakfast in anticipation of a great day of eating!

La Bergamote - croissants
La Maison du Chocolat - macarons, chocolate
Demel - Esterhazy torte, milchraum strudel
Cafe Sabarsky - Dobostorte, apple strudel, coffees
Andre's Hungarian Cafe - apple strudel, palacinsta
Lady M Cake Boutique - Milles crepes cakes, and the St. Honore.

My work's home base is in Switzerland. There, I discovered Thomy’s Senf. I thought at first, it was toothpaste, as it's sold in a tube (very portable). Thomy is a Swiss brand that produces food products such as mayonnaise, mustard, salad dressings, and the best [again in a tube] tomato paste. If you can get a tube of this Swiss equivalent to the U.S. 'every home has some' of French's Yellow, you'll love it. It's creamy and thick, has a nice sharpness and is packed with amazing flavor.

Raye’s “Down East Schooner” Mustard. It was also the gold medal winner in the 'Classic American Yellow Mustard' category at the 2009 Mustard Competition.

Maille regular and whole grain Dijon
Gulden's Spicy Brown Mustard
French's Yellow

Bertman's Ballpark Mustard - absolutely the best! (I live in CT but order it from OH)

Stonewall Kitchen's Blue Cheese & Herb Mustard, amazing flavors abound.

Maille Dijon, like many others have said. Though I also have developed a fondness for Grey Poupon coarse ground mustard, which I often use in my cooking as well.