Genius with a thick Irish accent: Garth Ennis, creator of Preacher graphic novel series
Genius with a thick Boston accent: Any number of people, I’m sure, who pock their cahhh in Hovad Yod, if you know what I mean. 
Genius with a thick New York accent: Can’t think of one off the top of my head, but New York City has way more smart and creative people than most of the South.
Genius with a thick California accent: Californians have accents? (Yes, I know they do sort of have accents/use terms that other regions don’t use, but not very recognizably).
Genius with a thick Australian accent: Australia was founded by what some might consider the bottom of the British gene pool (criminals and ruffians), so you make a good point that, like American Southerners, it would be difficult and rare to find a genius with a thick Australian accent. Also, the number of Australians that have achieved any significant recognition in the U.S. or elsewhere is sadly confined to only a handful, so far. However, Steve Irwin, despite lacking much higher education, was a liberal and an environmentalist, and knowledgeable about wildlife and biology. Also, if New Zealand counts (and yes, I know, New Zealand and Australia are NOT the same thing), then the two gentleman from the music group and TV Show Flight of the Conchords are talented, creative, and accomplished, though not exactly geniuses in their own right.
Geniuses with a thick Jersey accent: Funny enough, I Googled recently “What percentage of New Jersey is Italian?” and was shocked that the answer apparently is a mere 14.5%. Surprising, isn’t it (or maybe it’s just wrong…)? However, as I mentioned above, New York City has lots of creative, moderately intelligent or higher people in it, people who benefit from living in a city with every type of culture and mindset imaginable represented constantly in a kaleidoscope of expression, so I’m sure there are plenty of Jersey-accented people in the NYC metropolitan area who have significant intelligence and education.
Geniuses with a thick Minnesota accent: I’m to understand that movies like Fargo vastly exaggerate and misrepresent the way most Minnesotans speak, most of them not sounding like that. However, despite not being the cultural center of the US/ world like NYC or Seattle is, even the cold isolated Midwest North of the US is generally less ignorant, close-minded, and inbred than the Deep South.