The Dungeon of Doom is open year round, but the Hollywood Museum really sells it to the public during the Halloween season, renaming the attraction Monsters, Mummies and Mayhem: Your Worst Nightmares Come to Life. You can view the display of horror movie props, costumes, and posters any time during the museum's regular business hours (10am to 5pm, Wednesday through Sunday), but if you come in costume on the weekends of October 27-28 and November 3-4, you will receive a $5 discount off regular admission price.
The Dungeon of Doom's horror-themed collection is located in the Hollywood Museum's basement, appropriately enough, but the main floor has several displays from fantasy and science fiction films (Harry Potter, Elvira, Planet of the Apes, etc).
The Hollywood Museum is located at 1660 N. Highland Avenue in Hollywood. Call (323) 464-7776 for more information, or visit their website. (Warning: The Hollywood Museum is lax about updating their page for the Dungeon of Doom; there is out-of-date information from Halloween 2017 buried in the text.)
Regular ticket prices are: $5 for children 5 and under, $12 for students and for seniors over 65, $15 for adults.