Throughout the history of Middle earth, their have been many Dwarf realms. They were:
Khazad-dum. The most famous and greatest of all the others was Located in the Misty mountains it was the home of the Longbeards. It prospered for thousands of years until the Dwarves awoke the Balrog which drove them from Khazad-dum, it was then renamed "Moria" meaning "black pit" by the Elves.
Nogrod and Belegost. located in the Ered Luin Nogrod, being the home of the Firebeards and Belegost, being the home to the Broadbeams. Nogrod was totally destroyed during the War of Wrath and Belegost being ruined, leaving the firebeards and the Broadbeams to rebuild their halls and as many did, move to Khazad-dum.
Kingdoms in the Ered Mithrin.
The Iron Hills.