The Blue Ridge Parkway (from Asheville on north) connecting to Skyline Drive (through the Shenandoahs) are two of the most beautiful drives you can do. They parallel I-81, more or less, although the drive time will be dramatically longer. If you are doing the drive on a weekday, it'll be a lot quicker since you'll be traveling in peak leaf season, when the roads are jammed with slow-moving tourists. Still, it's worth leaving the interstate at least for a while to get these views on a nice day.

The Charlottesville/Staunton area would be a fine place to stop for the night--it's more or less halfway. Both are college towns and there are plenty of nice accommodations. I have not been to Staunton (pronounced Stanton, by the way) but have spent plenty of time in Charlottesville. The must-see thing around there is Monticello, Thomas Jefferson's estate, which is well worth a stop. There are plenty of interesting Civil War battlefields and monuments as well.

Speaking of which, right before you reach Lancaster you will go straight through Gettysburg, which is absolutely worth spending a few hours at if you have the time. It is pretty compelling.

There are tons and tons of things to see and do along that route, so you'll get lots of suggestions.