This winds up being a repeat of what Mike said, but here goes anyway. Chattanooga isn't far from me either. Some comments about the trip from Missouri to Chattanooga (assuming that you’re coming through Nashville and not Memphis):
Fort Donelson
http://www.nps.gov/fodo
I’m ashamed to say that I’ve never been to this one, a condition that I must rectify some day
.
Carter House (Battle of Franklin)
http://www.carter-house.org/
Carter House itself isn’t worth stopping to see except for some war scars left in the walls, but the museum behind it has a tremendous ACW medical exhibit and is well worth the trip.
Stones River
http://www.nps.gov/stri
Not a lot of money put into this park, but it is worth the visit since you’ll be driving by it on interstate. Its not the caliber of a Gettysburg, Antietam, Shiloh, or Vicksburg but you can get the feel of it in either a quick drive through (rent the tour tape) or walking the field.
Chattanooga/Chickamauga
http://www.nps.gov/chch
The Chickamauga service center is fantastic, but the Chickamauga park confuses the heck out of me. I don’t get my bearings until I reach the site of Thomas’ stand. I would be better off never leaving the service center. I’ve never ‘really’ visited the Chattanooga sites. When I go to Lookout Mountain, I generally always take the Incline Railway to Rock City and bus down the road to Ruby Falls. Oh yeah, there are some ACW sites up there somewhere, isn’t there!
Other non ACW recommendations for the trip include visiting or staying at the Opryland Hotel in Nashville (could catch a Grand Ol’ Opry show while you’re there if you go through on the right day) and routing back through Gatlinburg/Pigeon Forge which is Tennessee’s version of Branson, Mo except that Branson doesn’t have the Great Smokey Mountains National Park.
Lt Gen Ned Simms
1/1/VIII/AoS/USA
Blood 'n Guts hisself, a land lovin' pirate. Show me some arty tubes and we'll charge 'em.