the most common food items that i've heard were pizza pies and bagels from the ny/nj area stuffed into the trunks of their cars. i've even heard of someone taking two pizza pies and bringing them onboard a flight to california.
i was tempted to do this with bbq sauces while visiting the south but balked at the idea.
Does booze qualify as a food? It's easy to stock pile tax free booze at the strategically located New Hampshire state run liquor stores. They have become a travel destination for out of state customers.
When I visited my Dad in Florida I always stuffed a small suitcase with table talk pies, which are local and were unavailable in Florida. Ah So sauce too.
When Cape Cod potato chips first came out, they were only available in New England and I used to ship bags to my uncle in Virginia.
When I was in college in Virginia, when coming back to school from Massachusetts, I would bring several boxes of Ellio's Pizza, which were unavailable in Virginia.
When Yuengling was not available in Boston, I would bring a couple of cases back from Philadelphia when visiting friends from college there. It's been available here for awhile now, so that's no longer necessary.
Couple of Italian restaurants (not Olive Garden!) sell their own sauce (canned) so I’ve stocked up on that in the past.
I love Trader Joe’s salsa (and a few other sauces they carry) so I’ll stock up on those since I don’t live near a Trader Joe’s.
When I first moved to Florida every visitor used to come down with fresh NYC bagels, that we sliced and froze, several others used to bring a pizza from a favorite restaurant in Brooklyn, but over the years we’ve actually gotten some very good kosher and Italian food places opened up here in South East Florida starting on Miami Beach where there has always been good Jewish Deli Restaurants and Bagel Bakeries. Good Italian Food is also available and as developers built in Broward and PalmBeach Counties we have an abundance of excellent food and restaurants as well as specialty food markets, now its become very easy to get the most delicious meals in this area.
Not stockpiling, but we bring local food when we travel and bring back stuff from where we go. Most commonly requested items for us to bring from Maryland are steamed crabs and Utz potato chips. The crabs have to be packed in a sealed cooler to stay hot and not stink up the plane. When we go to New Orleans I always bring back shrimp/crawfish etoufee and gumbo, as well as local sausage, crawfish or meat patties and anything else that is local to NOLA and looks good. That stuff is frozen so we just pack it in our luggage in a soft sided cooler bag.
I never brought any-myself but in Chicagos O'Hare airport there were deep dish pizza being sold frozen and packed in insulated bags. Past security and all, so you could relatively easily take some on your flight.
Before Coors went nationwide it was a thing for people to fill up their trunks with as many cases as they could and drive them 800 miles to my home town. The cachet wore off pretty quickly once Coors became readily available. Also, my then GF would wrap some Ponzio's cheesesteaks in foil and plastic wrap and bring them in her suitcase when flying back from seeing her folks. Nobody in the midwest had heard of them then. It's still tough to get a decent one outside a 75 mile radius of Philadelphia.
My cousin in LA really likes Halal Guys here in NYC. So every time my aunt visits, she would get like 4 boxes of their chicken and rice and beef and rice and take it back to LA for him.
BBQ sauce makes more sense than Bagels, which really are best fresh.
There are regional sodas that are fun but super expensive to ship.