The short version
You have a real kitchen here, so a lot of guests skip the daily restaurant grind and cook a few meals in. The closest full-size grocery is the Whole Foods on Third Avenue near 59th Street, about a 7-minute walk south from our door at 341 East 62nd Street. It's open 7am to 10pm, seven days a week. For the in-between stuff (a forgotten phone charger, late-night ice cream, coffee filters) there's a tighter network of smaller markets and drugstores right around us. Here's how we'd handle it.
The full grocery run: Whole Foods on Third
For a proper shop, walk down to the Whole Foods on Third Avenue between 58th and 59th. It's the Lenox Hill store, open 7am to 10pm every day, and it's the easiest place to fill a fridge from empty: produce, meat and fish counters, prepared foods if you don't feel like chopping, plus the usual pantry basics. From us it's a straight shot down Second or Third, roughly a 7-minute walk. If you'd rather not carry it, they deliver through the Amazon app, which is what we'd do for a big first-night order while you're still in transit.
If you want a second option a bit further out, the larger Whole Foods at 86th and Third is a longer walk or a short hop up the 4/5/6, but for most stays the 59th Street store is the one.
The quick run: Morton Williams and corner markets
For a small basket (eggs, milk, a bottle of wine, something for breakfast) you don't need to go that far. Morton Williams runs several Manhattan locations, and a couple of them stay open 24 hours, which is the move when you land late and want real food in the apartment instead of a vending machine. There are also smaller delis and corner grocers scattered through the East 60s. They're fine for the basics and a coffee, less so for a full week's shop.
My honest take: do one real Whole Foods run when you arrive, then use the corner spots for top-ups. You'll cook more and spend less than you think.
Late-night and the pharmacy
For a pharmacy, the Duane Reade and CVS locations along Third and Lexington in the East 60s cover the basics: over-the-counter meds, toiletries, a phone cable, a bag of chips at 11pm. Some run 24 hours, some close around midnight, so check the door if it's very late. These are also your fallback for the small things you didn't pack, which is usually a charger, contact solution, or sunscreen in summer.
If something runs out in the apartment itself, text me. I'd rather point you to the closest open shop than have you wander.
What we'd grab the first night
If you want a starter list for the first trip: coffee and milk for the morning, eggs and bread, fruit, something easy for dinner you can cook on the range, a bottle of whatever you drink, and a few snacks. That's a 15-minute Whole Foods run and it changes the whole stay. You wake up, make coffee in your own kitchen, and ease into the day instead of hunting for a table.
A note on the kitchen
Every apartment here has a full kitchen, not a kitchenette in the corner. We chose the cookware ourselves, so you've got real knives, pots, and pans to work with, not the bare minimum. Stay three nights or three weeks, it's your apartment, and the kitchen is a big part of why people settle in. Cook as much or as little as you want.