Mr. Dolan, 68, oversees a family empire that includes some of New York's most famous brands, including Madison Square Garden and Radio City Music Hall, the Knicks and the Rangers. At the epicenter of professional sports, marquee concerts, politics and real estate, he is one of the most powerful forces in the city. He is also one of New York's most vilified public figures, a punching bag and a punchline.

But New York is not where his brain or his video monitor are focused. Mr. Dolan — son of Long Island, commander of beloved New York sports teams, and magnet for the type of caustic mockery that only New Yorkers are capable of expressing — is looking 2,500 miles southwest for respect, redemption and reputational rebirth.

Foremost on his mind, and on the live-feed beamed into his New York office, is his new arena in Las Vegas, an audacious project that he believes could revolutionize the live entertainment industry.