Yes, they do film ghost stories at genuinely haunted (and scary) places. It’s happened many times.
It was filmed at Ettington Park Hotel, near Stratford-upon-Avon (England).
It’s supposed to be delightfully haunted. The hotel is elegant and reminiscent of the famous movie. And, according to some, it’s home to at least one ghost.
Here’s a 7-minute video about Ettington Park’s ghosts.
That YouTube video of Ettington Park Hotel is at: https://youtu.be/-FpczWUHUng
Trivia: That movie’s original – and perhaps haunted – spiral staircase reappeared in the 1999 remake of The Haunting, and the Netflix series, as well.
Another old movie, Hush, Hush, Sweet Charlotte, wasn’t exactly a ghost story, but it was chilling. They filmed it at Houmas House, one of Louisiana’s most haunted houses. (I’ve spent the night there and can verify that it has ghosts that appear, day and night.)
Here’s a one-minute ghost story from Houmas House:
That Houmas House video is at YouTube, at: https://youtu.be/fac0ctSq_eQ
Not far away, several movies were set in St. Louis Cemetery No. 1, at the edge of New Orleans’ French Quarter. They include Easy Rider and Cincinnati Kid. Producers filmed Interview with the Vampire at other haunted New Orleans locations.
Here’s a two-minute video about the ghosts of St. Louis Cemetery No. 1:
That NOLA video is at: https://youtu.be/t-xKe7s6eMY
The Hollywood movie set for the original movie, Psycho, was supposed to be haunted. I’m not sure if paranormal encounters happened before, during, or after the initial filming. At night, people were visible near upstairs windows… when there was no floor to walk on, and no possibility of a light near the window, either.
Those may be urban legends, but I heard enough first-person stories to think they might be true.
Session 9 was filmed at Danvers State Hospital, Danvers, MA (USA). The former hospital and the town of Danvers have many ghost stories, often overshadowed by nearby Salem.
Here’s a 42-minute video about Danvers State Hospital, featuring Brian Cano (of “The Haunted Collector”). I know Brian in real life, and respect the research shown in videos like this one… where Brian was in control of the editing. (I wasn’t so impressed with the “Haunted Collector.”)
That 2008 video about Danvers is at: https://youtu.be/HkQAPVJ-RrI
The haunted Yankee Pedlar Inn in Torrington, CT (USA) inspired – and later became a set for – The Innkeepers.
I’m sure you’ll find many other movies listed, online. Look for “movies filmed at haunted places.”