Since we are further east, cannot comment on I77 vs I95. We have found the easiest/quickest between Richmond (I95) and Syracuse is I81 to I66 east to US17 south to I95. Take I295 around Richmond. This way you avoid the DC traffic. I have driven around Richmond many times and only once or twice encountered traffic, and that was due to an accident.
I've never had luck finding much of anywhere to stay between Syracuse and Harrisburg, so that might be your longest haul. Places we have stayed and would stay again include Western Village in Carlisle PA, Falling Waters WV, Candy Hill Winchester VA, RV Resort at Carolina Crossroads at Roanoake Rapids on 95 (Passport America), Bass Lake Resort Dillon SC (also PA), McIntosh Lake Townsend GA, Coastal Georgia RV Resort Brunswick GA, Crooked River State Park St Mary's GA, Walkabout Woodbine GA (also PA).
Another alternative is to travel from Syracuse to Corning, then US15 south to pick up I81 near Harrisburg which might add 20 miles to the trip. We decided to travel this route this summer to try the COE campground in Tioga PA.
We have had good luck mapping out the route and checking out campgrounds on
rvparkreviews.