Between hotels, restaurants, and gas stations that simply wouldn't serve black people and a confusing patchwork of "sundown towns" and differing Jim Crow laws, it seems like long-distance travel (by car, train, or bus) would have been extremely difficult and potentially dangerous.
How did African American travelers know where to go and what to expect?
African American writers published articles & travel guidebooks addressing this very concern. The most famous was the Negro Motorist Green Books, named after its publisher Victor H. Green, a postal worker and veteran from New York.
Inside were classifieds, hotel listings, travel routes, friendly locations and general advice for African American tourists and travellers. Starting as a 16 page pamphlet, it eventually evolved into a 100 page manual. Its tagline of "Carry your Green Book with you. You may need it..." highlighted the very real risks and dangers of African American travellers. The entire archive is available from the New York Public Library.
Independent leisure travel in cars was of course only possible for African Americans with the means to do so. The primary method of transport were still trains, travelling in "Jim Crow cars" that were purposely offered an inferior travel experience. An example is still preserved at the Smithsonian’s National Museum of African American History and Culture
The Warmth of Other Suns is a brilliant piece of narrative history looking at 3 or 4 case studies from the Great Migration. It goes into detail about how a sharecropper family actually had to plan their escape to prevent the white landowner potentially interfering with it.