I stick by Antietam. Its extremely moving, epic skirmishes occured there in places like the corn field, the sunken road, and burnside's bridge, and there's photographic evidence of the carnage that occured in those places so you really get the feeling of what it must have been like, defending the sunken road when the union boys started pouring over the ridge only yards in front of you and what must have been going through their minds.
Antietam is the site of the bloodiest single day in American history. It stopped Lee's first invasion of the north, and mostly sealed the south's loss by discouraging foriegn intervention. So the importance is definately there, and what makes it a great destination is that its compact compared to a place like gettysburg, and its lesser known. I had the chance to hike it one drizzly spring morning last year, and we were nearly alone. Oh, and the land it occured on is simply beautiful. Just the solemn feeling of walking burnside bridge in the rain was enough to justify taking a civil war vacation over the traditional beach scene.
If you're into battlefields and American history Antietam is just awesome.