The now-defunct Klondike Hotel and Casino at 5191 Las Vegas Boulevard is where they filmed those scenes. Also known as the Klondike Inn, the Vegas Strip casino had roots in 1962, and in 2004, the Royal Palm Las Vegas purchased the premises.
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Vegas Vacation filmed at The Mirage (I'm sitting with Beverly D'Angelo as Siegfried & Roy turn Chevy Chase into a tiger) and the Golden Nugget with scenes at the Hoover Dam, Casa de Shenandoah, Neon Museum, and the MGM Grand.