Azkaban is the only prison mentioned period. No other prison has ever been mentioned, unless you count Moody's trunk, which was used to imprison Moody himself for the better part of a year.
The only thing similar to Dementors that has been mentioned are Lethifolds, which are likewise immune or highly resistant to everything but the Patronus charm, and the Augurey, a raven like bird with a cry could drive people insane after enough exposure. The first is a carnivore, the second is not.