Colbert, Washington was named after the postmaster in 1902. Prior to that, it was called Dragoon. Dragoon was the name of the creek that ran through the area. This area was a major trade hub for the town because of its location on the Spokane River, right off Oregon Trail. This brought in new settlers on a regular basis. Most just stopped for a little while before moving on to other places to settle permanently. Mining, and later foresting, were both major sources of income for Colbert. Workers would escape to Colbert to raise their families.
The historic town of Colbert does have some dog-friendly amenities, including some beautiful walking trails that will take you along the mining lanes. They can be dangerous and are only open during the summer months. You are never allowed to go in the mine, but you can walk your leashed dog along the paths. Some of them have historical markers along the way. You can find a complete map at the visitor center in the main hall.
If you would like to venture out a little ways, visit the city of Spokane with your pup. There, you'll find many more conventional amenities for dogs and owners, including parks, restaurants, and trails.