Depending on the weather, leaves will peak at different times. Since you are coming from Calif. and want to see various regions (Smokies, D.C., etc) I would just go, take my chances and watch web sites that list fall color peak days and try for sites in that region.
That said, we booked a campsite in Wears Valley (Smokies - near Pidgeon Forge) and paid the monthly rate (usually a month rate is about the same as two weeks). This gave us all of Oct. to explore out from the one area and wait on the leaf change. They didn't really change till near the end of Oct. in fact it went from peak color to freezing rain & snow in two days with many trees down from the weight of leaves and snow. Very unusual.