I called my brother, who was a Highway Patrolman in KC for over 30 years. He said the BBQ joints around the stadium are only 'money pits' that don't know what BBQ is. He agreed with me that the best place is
Arthur Bryant's Barbecue, on the corner of 18th and Brooklyn. They also have one at the Ameristar Casino (close to where my sister lives) but Larry swears it isn't as good.
The address is 1727 Brooklyn Avenue. From the stadium, go west on I-70 a few miles to Prosepect. Don't worry, traffic moves FAST except at rush hour. Shouldn't take but a few minutes. Take the Prospect Ave. exit, turn left (south, just in case the roads have changed) to 18th Street. Turn right, go about 3 blocks to Brooklyn. The restaurant should be in the northwest corner.
One word of advice: Do NOT leave anything in your car, lock the doors, and go during daylight. A friend of mine, "Cheese", used to run a beauty school off of 23rd and Troost, about 15 or so blocks southwest of there. I had no problem going into that neighborhood, and it's a LOT rougher than where AB's is at. Still, you see a car with out of state tags....
Stay away from Gates BBQ. In the 70's it was good, but then the Trotter family sold out their half, and the current owners know more about making money than barbecue.
Have fun....last time I was in Kaufmann was when Freddie Patek was still on the team.