There's a town that I've stopped at a couple of times on my way to Montreal called Derby Line,Vermont.It's right on the Quebec border (and right off I-91) and it features a couple of interesting things.One:the Haskell Library.It was built,intentionally,right on the US/Canadian border as a gesture of international friendship.You enter via the US but much of the building,including the checkout desk,is in Canada.Most of the books are in English but many are in in French (because it serves the Quebec town as well).
Two: "Canusa Avenue" ("Canusa" as is Canada and USA).There's a stretch of that road where the pavement itself is entirely in Canada but a few of the houses south of the pavement are in the US.Those people,whenever they leave their driveway,must report to Canadian immigration,which is right down the street.I've driven that street (out of curiosity)...pretty cool,IMO.
And in New Orleans you have to drive east over the river bridge to get to the West Bank.
.... and South Claighborn and South Carolton cross at 90 degrees.
It is New Orleans
Two years ago, while on vacation in Maine, we visited Campobello Island. The island is entirely within Canada but the land link it into Maine. During the summer, a ferry operates that links the island with other Canadian islands that have land connection to the rest of Canada. The island has no hospital, no bank, no grocery store. For that, they must all cross the border into Maine.