I did a Google search for "John Wayne Dude Ranch" and these two where at the top of the list...
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Hacienda del Sol Guest Ranch Resort
In 1948, Hacienda Del Sol was converted into a guest ranch that immediately attracted the Silver Screen's most notable stars, among them John Wayne and ...
http://www.haciendadelsol.com/ -
Flying L Guest Ranch in the Texas Hill Country
The Flying L Ranch transports you back in time to when Hollywood legends like John Wayne and Erol Flynn made this spot their hideaway. ...
http://www.flyingl.com/