I did this drive in reverse, from MS to Philly. Make sure to take The Blue Ridge Parkway through the Appalachians.
I would suggest starting out along the coastal route ( and running on the beaches in MD.) rather than driving inland. Then head west to the mountains.
I would also, unless you are a glutton for punishment, avoiding the congestion when driving through the DC area.
Jefferson’s Monticello is worth a stop and a tour, however.
Too bad that this is not a very pretty time of the year for this trip..although things will get more spring-like as you head south.
If you look at the Rand-McNally atlas, it will have the scenic drives and hot spots marked.