"Troll - in the dungeons - thought you ought to know."
-- Quirinus Quirrell
Beneath the ground floor of Hogwarts castle are found many passages, dungeons, and chambers. Some of these are easily accessible from doors that open off the Entrance Hall. Others are hidden and can only be entered by magical means.
The dungeon passages and rooms under the castle have stone walls and are lit by torches. Nearly Headless Nick held his Deathday Party in one of the “roomier” dungeons (CS8).
Other known underground areas of Hogwarts:
Descending by staircase from a door in the Entrance Hall, students will arrive at the Potions classroom, next to which is Snape’s office. The Slytherin common room also appears to be connected to this dungeon entrance. Another door in the Entrance Hall leads to the kitchens and the Hufflepuff common room. The chambers where Dumbledore hid the Philosopher’s Stone were accessible through a trapdoor on the third floor (which would suggest a fall of at least fifty feet down to the tangle of Devil’s Snare — one hopes that there magic involved to keep explorers safe when they land). The mysterious Chamber of Secrets can only be accessed by a magical entrance which requires the use of Parseltongue.