That was the whole sketch. No, I don't get it, either.
I've lived in New Jersey my whole life, which is more than a short time. I've been to every corner of the place, met lots of natives, defended it when it needed defending and decried stupid politicians (like some New York city mayors and our own current governor) who seem to look down on us. I've heard all sorts of opinions, lived through countless "what exit" jokes, been expected to chuckle when it's suggested that most of our residents are in the mob and the rest live on a toxic waste site.
But I've never, EVER, heard anyone from here say "Joisey."
Not once. Zero times. Never. And believe me, I would have noticed. I keep an ear out for such things. Nobody from New Jersey actually talks like that when we're not consciously trying to be ironic. Granted, some of you from more straightforward states might not understand NJ Irony, but you can trust me when I tell you: We don't EVER say "Joisey" seriously.
In fact, the only people I've ever heard say such a silly word are Manhattanites who think they're being clever and condescending, and Brooklynites, who actually talk like that.
Even the cast of "Jersey Shore," while completely trashing any chance we had to rehabilitate a false image of the state, don't say "Joisey." And I'd like to point out, only two of THEM are even from the Garden State (See? Even our state nickname is ironic!).
When I meet someone from, say, Arkansas, I try very hard to say the name of the state the way they'd say it. If I'm talking to a persona from Texas, it's possible we'll allude to some political differences (or not), but at least I'm still perfectly capable of saying "Texas" properly. I like to think that if I ran into an Oregonian, I'd try to pronounce the name of the state the way they say it should be pronounced, which sounds to me like "Origun," because I figure they know better than I do. If corrected, I will accede to the native on such a point.
So do me a favor and--just when you meet me--don't say "Joisey."
There's no such place.