lord of the rings - Were there any jails or some type of incarceration centers in Middle Earth or Tolkien's universe?

Well the Valar held courts in Aman the Blessed Realm at place called: Mahanaxar the Ring of Doom where they judged the criminal cases and often held councils. We are also told that after spectacular Battle of the Powers (which echoes were perceived by elves at Cuivienen hundreds and hundreds of miles away as great flashes of light and earthquakes) that Morgoth was put to prison meaning into the Halls of Mandos (also chained by the very special, made for that very purpose Angainor, the chain made by Aule, apparently magical).

When someone's imprisoned in the Halls of Waiting, there's no escape (for those who don't know Halls of Mandos are a place for the spirits of the dead of all races, but mortals stay there only for unspecified amount of time until they leave permanently to whatever fate that awaits them, it's also the dwelling place of Vala Namo also called Mandos it has apparently semi material location in Aman in land of Valinor where also all other Powers have their physical dwellings, but Halls of Mandos appear in the same time semi spiritual and they grow over time, possibly there is a connection to the Unseen the spirit or shadow world, second layer of reality besides the visible world, a plane where wraiths and spirits exist and roam freely, as well as there are certain things native to it ,,signs and forms that are hidden to us", ,,things in worlds invisible to mortal men") anyway returning to topic.

We know that Elvenking's Halls in Mirkwood were not only a stronghold, refuge for elves, storage, treasury and royal palace but also dungeon for prisoners (and to add something, don't worry if you ever get to this elven prison, elves treat even their greatest enemies very decently once they capture them :):) ), another prison facilities are of course the great fortresses of the Enemy, Dol Guldur and Barad-dur (nobody ever escaped Barad-dur unless released on purpose or to last trip on death sentence in Shelob's Lair) and there is of course famous Angband the Hells of Iron, where thousands of slaves were performing hard labour, as you can summise those places hardly have anything in common with ,,justice" or ,,law enforcement" unless in twisted minds of their masters. We also know that Eomer was imprisoned in Edoras for threatening Grima, king's advisor, with death in king's presence (so there must have been a dungeon or something similar in the city, maybe even in Meduseld itself), it is also reasonable to assume that other cities or strongholds of various peoples would have facilities for keeping imprisoned criminals. As for general law enforcement in Middle Eaeth that's a different question altogether, we know that wanted criminals can have a price on their heads, they are judged either by local king or other authorities (like great gatherings among people, so called moots like men of Brethil did).