New Yorker here. Unless the grads you're talking about are extremely unusual--and perhaps they are!- -they'll be like most NYC residents--relying on foot power and public transportation, not a car. People here shop in the grocery stores closest to them
There are plenty of chain grocery stores in NYC. But if a store isn't convenient to where you live, you're probably not going there. Because you probably don't have a car. And even if you do have a car, you're probably not using it to go to the grocery store.

Best posts. Fellow NYer here, so I'm the same. As much as I'd like like to consider myself unique, unusual, different, etc.,

when it comes to buying groceries, I shop at the closest grocery stores. There is a D'Agostinos further away with better sale prices, but I usually don't have the time or the impetus to WALK that much further away and lug back four heavy bags of groceries.
This was my trip the other night after coming back from a movie premiere party : I already have my backpack with me. (Always do.) I prefer a backpack to a handbag slung over one shoulder which offsets my weight on one side and slides off my shoulder, even though I am decades beyond being a college student. Once the backpack is stuffed full with some things I've bought and put on my back, it leaves
both hands free to carry whatever else I am buying - typically 2 (evenly weight distributed) bags. A very usual question the cashiers bagging the groceries will ask is, "Do you want it all in one bag or two?" as they know it's easier to walk & carry two evenly distributed bags than walk lopsided with one heavy bag.

I usually end up with 4 bags - and those may be stuffed with smaller bags from other stores along the way.
I never have one of those collapsible shopping carts. I'm not at the old granny stage yet to need one, nor do I want to lug around a large, cumbersome, heavy, collapsed cart around all day or TO the store. It's like carrying around a piece of luggage. PLUS, I didn't know I'd be stopping at the supermarket after the party. Once filled, the carts are hard to negotiate through all the tourists, local pedestrians, bicyclists & street traffic, up & down curbs and around pot holes and bicycle lanes. And the carts tend to make a lot of noise. It is quicker & easier to just lug shopping bags home. I would think two, able-bodied 22 yr olds would think the same way.
I bought enough groceries to fill 2 plastic grocery bags. Then I decided to stop at the drugstore to pick up my favorite brand of toilet paper that is on sale this week. I WANTED to get four 12-packs of the toilet paper. But, since I already had 2 bags of groceries, I could only lug home two 12-packs. (One 12-pack & one grocery bag in each hand. Weight evenly distributed.) While I
could have carried an extra 12-pack in each hand, as they aren't that heavy, they are wide and cumbersome, which make them even harder to negotiate.
So that means a
second trip to the drugstore before the sale is over by the end of the week. And probably another trip to the supermarket, as I only have a half size fridge and minimal storage space - hence why I only got 2 grocery bags full earlier.
This is my weekly routine. As well as is the routine of most NYers here in the city. Shopping a couple/few times a week as we come home. Since I'm already out, I might as well pick up the extra things I need, in small, manageable amounts,
from the stores closest to me.
If the nearest Trader Joe's, for example, is 40 blocks away, they won't be shopping there, no matter how appealing the merchandise is.
I love Trader Joe's, but I'm not often in those neighborhoods. To just make a trip there only for Trader Joes, means $5.50 round trip subway fare. I don't have a monthly unlimited card as I walk everywhere I can. When I do go to particular neighborhoods, I tend to multi-task and hit ALL the stores in walking distance that I need to visit in that neighborhood at once. If I'm in Chelsea, that means I'll hit Home Depot for the odds & ends I need, Michaels and Dick Blick for art supplies, Staples for an extra hi-lighter, maybe Old Navy or Bed, Bath & Beyond, before heading over to Trader Joe's last, as almost everything I buy there is frozen stuff. I also plan my route so that I am buying the lightest/fewest items first and pick up more/heavier items as I go along. That may mean I already have my hands (and backpack) full by the time I head into Trader Joe's. And that again will determine how much I buy there. Also, not only do I have to lug everything walking, I have to negotiate stairs and a subway car crammed full of people, too, if it's rush hour,


fit everything in without banging into other people, set the bags down, (there usually is no seat,) and scoop & lift all my packages easily and quickly at my stop. Also, the closest subway to a store may not necessarily be the closest subway home. EXTRA walking.
Fairway: I've made a pass through there a few times as people keep raving about that place. But, other than the assortment of fresh veggies and artisan cheeses, they are like other supermarkets, but with even narrower aisles. I think I've maybe actually
bought things in there 3 times

and they were the Fairway brand spices. I have a farmers market in my neighborhood and can get artisan cheeses in my own neighborhood. And I don't have to deal with the long lines at Fairway. Plus, Trader Joe's is down the street from them now, so I'd rather shop there.