Martin Luther King Jr. not only had a Dream, he had places he lived. One such place was his birth home in Atlanta, Georgia. Fortunately, you can tour the home as it is a National Historic Site maintained and operated by the National Park Service.
You want to take the tour, according to the Parks Service, to get the most out of your visit. There are other sites nearby related to Dr. King which you can also see, and those are self-guided.
There is also the home in Montgomery, Alabama, which was bombed in 1956 and in 1957. That home was the parsonage for the church that Dr. King was the pastor of, and was owned by the Dexter Avenue Baptist Church. It was targeted for violence after Dr. King emerged as a leader and organizer of the local bus boycott, a boycott widely considered to be the launching event for the modern civil rights movement. The home is now a museum.
So, both of these places are open to the public and would be worth a visit if you are ever in Montgomery or Atlanta.