My son will be in EAstern Kentucky for the next few days--flew into Cinncinnati--what should he not miss here

Does he like to hike? Honestly, with the exception of the great outdoors, there's nothing to see in Eastern Kentucky.

If he can venture to Lexington, the Kentucky Horse Park is nice if one likes horses.

What exactly do you mean by "eastern Kentucky"? There is more to do in this part of the state than just hiking, but some of it depends on what section of the state your son is in. If you can be a little more specific about what cities/towns he will in, I can probably help.

TO TELL YOU THE TRUTH AT THIS POINT ALL i KNOW HE IS STAYING ABOUT HALF AN HOUR FROM CINNCINNATI--ACROSS THE STREET FROM A RACETRACK. DOES THIS SOUND FAMILIAR? HE IS THERE FOR SOME SPORTS EVENT WITH ESPN--50 STATES IN 50 DAYS!

That's not Eastern Ky that's Northern Ky and Southern Ohio. Plenty to do depending on what he likes. There are threads on this board you can search but some of the highlights would be:
Reds Baseball
Cincinnati Zoo
Newport (Ky) on the Levee
Newport Aquarium
Cincinnati Art Museum (my favorite)
Cincinnati Museum Center
Sawyer Point
Kings Island
Lots of golf
much more

Also Gekko,
I disagree with there being nothing in Eastern Ky. There is a lot of beautiful scenery, especially Natural Bridge State Park and Red River Gorge.

Agree with poster about Kentucky Horse Park-very interesting. Churchill Downs in Louisville has good museum also. Louisville Slugger place in Louisville might also be of interest. Keeneland is the track in Lexington-hear it's beautiful (along with the beautiful horse farms in the area).

If he is in the more rural areas, the Kentucky park system in impressive. Each has good lodging and food and, depending upon the size, outdoor activities such as horseback riding and swimming. Mammoth Cave may be too far but that's pretty cool also.