What authority, under the Constitution does Congress have to say a small diner can't have separate seating for whites and blacks?
Interstate Commerce Clause.
If you ever get the opportunity in your life to speak to an older black person that lived during Jim Crow ask them how hard it was to travel. You couldn't just assume whatever dinner, hotel, motel, etc. you found on the highway would have adequate facilities for you and your family.
I used to think Black History Month was pointless but I am beginning to see its value. Listen to some of the stories about black musicians, athletes, and entertainers from back in the 50s and 60s. When on the road it was a pain in the ass trying to find a place to eat and sleep.