If it's a nice day, you could go the other way - to Weston, Missouri. Or for that matter, to St. Joseph (that may be cutting it close, however).

To drive to the Plaza (or to the museums nearby), you will need to have some understanding of the road system in Kansas City. After you pass Municipal (downtown) airport, cross the Missouri River on the Broadway Bridge, and bear right toward I-35 South. Stay on I-35 toward Wichita (not Topeka or St. Louis) until you come to Southwest Trafficway (not SW Blvd). Follow the Trafficway, also known as Summit, several miles until you come to a steep hill around 47th Street. At the bottom of that hill, you proceed straight (do not merge right) across a divided boulevard and Brush Creek. Left onto Ward Parkway, and from there you will see the Country Club Plaza. I recommend parking there and walking. The Nelson-Atkins is about fifteen minutes walking distance (to the East on Brush Creek Blvd/ 47th) from the Plaza.