The interior scenes at the Silver Mustang Casino floor in Las Vegas, Nevada were actually shot at  located at 49500 Seminole Drive in Cabazon, California.
Below are several reference photos of the casino floor as seen in Parts 3, 4, and 16 in Twin Peaks on Showtime.
Please note – this article is a work in progress but hopefully the images below will help my fellow Bookhouse Boy in the desert [swipes temple].
PART 3
PART 4
PART 16