I have looked at all of the major cinema chains and the AMC Theatres is the only one that is currently showing The Neon Demon on their ‘coming soon’ page. You can go to AMC’s website and type in your location to see if it will be playing at a location near you when it gets closer to June 24.
At this point, I am not seeing any info that indicates the scope of the release but I suspect it will be limited.
The Wichita Eagle is reporting that The Neon Demon will be playing at the east Warren Theatre in Wichita, KS for those who are interested.