There has never been a casino called Rodney’s Place, but there was a comedy club at the Tropicana with that name that was hosted by Rodney Dangerfield. It was one of a handful of comedy clubs that came and went in those days (the DVD "Opening Night at Rodney’s Place" dates from 1989 and features Tim Allen and Jeff Foxworthy, along with "surprise guests" Sam Kinison, Rich Little, and Heather Thomas). The effort didn't last, though it was succeeded by the popular Comedy Stop.
Dangerfield was a long-time regular in Las Vegas, performing in most of the big showrooms around town. Another Rodney’s Place-like show was taped at the Aladdin and is available on DVD.