Upper West and East:

Eli’s Manhattan * 1411 Third Ave. Between 80th & 81st (gourmet grocery haven - spendy but you'll be on too much of a natural high to care)
Café des Artistes 1 W. 67th (Great place for Sunday brunch, pre-theater)
Popover Café 551 Amsterdam Ave. Corner of 86th (Close to the Museum of Natural History. See my review here)
Between 59th & 23rd:
Campbell Apartment In Grand Central Terminal (drinks only, no jeans or sneaks, very "old New York". I've only been on Saturday nights - the jazz band is old school...in a good way)
Rare 303 Lexington at 36th (expensive, high-quality burgers and some of my favorite fries in the city. You can even top your burger with truffles!)
Gaby 45 W 44th Street, in the Sofitel hotel (pricey, perhaps overly so, but one of the most memorable meals of my life here. Quiet, soothing atmosphere.)
Ginger Man 11 E. 36th St. between 5th and Madison (avoid this place at night unless you reserved the private room or you don't mind crowds - on the other hand, sitting on the couch, drinking a beer at 2pm on a Saturday is sublime. Try the pretzel with the spicy honey mustard sauce. Here's my review.)
Shake Shack Madison Square Park (you'll wonder if the line is worth it for burgers and shakes. Yes, it is.)
23rd to 4th:
Chelsea Market 75 Ninth Ave. between 15th & 16th (Food shopping, restaurants, desserts, coffee, bread...this place has it all. Check the list of events - watching people tango right there in the market is truly a NYC experience)
Billy’s Bakery 184 Ninth Ave. (Take my word for it - skip the hype and tourists at Magnolia and come here instead for the best cupcakes in NYC)
Union Square Greenmarket (go before 10 a.m. on Saturday to see the chefs and locals, and to actually talk to the purveyors; avoid it after noon, unless you don't mind insane crowds)
Fig and Olive 420 W. 13th between Ninth Ave. & Washington St. (there are other locations, but I've only been to this one in the Meatpacking District - check out my post about it here)
Below 4th:
Home 20 Cornelia St. (one of my favorite places - cozy, casual, great food - but I haven't been there since the owners have changed. The patio is the best place for a warm summer evening!)
A Salt and Battery 112 Greenwich Ave. between 12th & 13th (it's been awhile but I have nothing but fond memories. They recently went local/sustainable, and the shop feels like a little piece of London here in NYC.
Between 59th & 23rd:
Campbell Apartment In Grand Central Terminal (drinks only, no jeans or sneaks, very "old New York". I've only been on Saturday nights - the jazz band is old school...in a good way)
Rare 303 Lexington at 36th (expensive, high-quality burgers and some of my favorite fries in the city. You can even top your burger with truffles!)
Gaby 45 W 44th Street, in the Sofitel hotel (pricey, perhaps overly so, but one of the most memorable meals of my life here. Quiet, soothing atmosphere.)
Ginger Man 11 E. 36th St. between 5th and Madison (avoid this place at night unless you reserved the private room or you don't mind crowds - on the other hand, sitting on the couch, drinking a beer at 2pm on a Saturday is sublime. Try the pretzel with the spicy honey mustard sauce. Here's my review.)
Shake Shack Madison Square Park (you'll wonder if the line is worth it for burgers and shakes. Yes, it is.)
23rd to 4th:
Chelsea Market 75 Ninth Ave. between 15th & 16th (Food shopping, restaurants, desserts, coffee, bread...this place has it all. Check the list of events - watching people tango right there in the market is truly a NYC experience)

Union Square Greenmarket (go before 10 a.m. on Saturday to see the chefs and locals, and to actually talk to the purveyors; avoid it after noon, unless you don't mind insane crowds)
Fig and Olive 420 W. 13th between Ninth Ave. & Washington St. (there are other locations, but I've only been to this one in the Meatpacking District - check out my post about it here)
Below 4th:
Home 20 Cornelia St. (one of my favorite places - cozy, casual, great food - but I haven't been there since the owners have changed. The patio is the best place for a warm summer evening!)
A Salt and Battery 112 Greenwich Ave. between 12th & 13th (it's been awhile but I have nothing but fond memories. They recently went local/sustainable, and the shop feels like a little piece of London here in NYC.

Gray’s Papaya Various locations (some people may disagree with me, but I say skip Papaya Dog and Chelsea Papaya. Stick with Gray's. For better or for worse, a NYC institution)
Oliviers & Co. 249 Bleecker St. (so, okay, I know it's a chain, but I fell in love with this store instantly when I entered. The staff is unpretentious and friendly, and you get to sample oils and vinegars before buying. Don't want to haul those bottles around? They'll ship for you. There's also a location in Grand Central Terminal)
Eat, drink, and visit NYC
Oliviers & Co. 249 Bleecker St. (so, okay, I know it's a chain, but I fell in love with this store instantly when I entered. The staff is unpretentious and friendly, and you get to sample oils and vinegars before buying. Don't want to haul those bottles around? They'll ship for you. There's also a location in Grand Central Terminal)
Eat, drink, and visit NYC
* Note: Yeah, that's right - I left off Zabar's. I've only been there once, very briefly, and I haven't been motivated to return. I found the space claustrophic in a way I've never experienced and, because of all the people and lack of space, everyone seemed to be ruder than usual. Not a good experience for me. Let me know if you've had a better one. Eli's was infinitely more enjoyable.