Erebor, the Iron Hills, and the Blue Mountains are the only three that we know dwarves lived in at the end if the third age (Thorin lived in the Blue Mountains for a while after Erebor was destroyed). Dwarves did at one point live in the Grey Mountains as well, but most (if not all) were driven out by cold-drakes. The survivors founded the Iron Hills.
Edit: There were seven dwarven fathers, who each began the main dwarven clans. One awoke at Mount Gundabad (Northern Misty Mountains),
two awoke in the Blue Mountains, and four awoke in the Red Mountains, far to the East.