Final answer:
The term 'Exodusters' is most closely associated with the post-Civil War movement of African-Americans to western states in search of freedom from discrimination and better economic opportunities, with Kansas being a notable destination.
Step-by-step explanation:
The phrase most closely associated with the migration of African-Americans to western states like Colorado, Oklahoma, and Kansas after the Civil War is a) Exodusters. This term references the biblical flight from Egypt and describes the journey of African Americans fleeing the oppressive conditions of the Jim Crow South. Notably, Kansas was a significant destination for these migrants, with over 25,000 Exodusters arriving there in 1879-1880 alone.
The migration was a quest for political, legal, and economic freedoms that were denied after Reconstruction. As a result, some of these courageous individuals had to endure various hardships and opposition from both Southern and Northern whites during their relocation. While some became farmers, others worked as cowboys or served as "Buffalo Soldiers" in the American West.