I have to ask why? Because the list is so extensive it will take a very long time to complete. A general rule would be easier.
State parks without power
Most NP unless run by concession
About 1/2 COE parks
Most NF campgrounds
But in case you are trying to compile it anyhow, here are the 69 campgrounds (out of 210) I have stayed at since 2004 that did not have power:
Campground City State Type
Wawona Yosemite Valley CA NP
Outside Okefenokee Fargo GA BD
Reedbinham Adel GA SP
Rood Creek Florence GA ACE
St Mary Boondock St Mary's GA BD
Wilderness Trail (North) Middlesboro KY BD
Wilderness Trail (South) Middlesboro KY BD
Fort Frederick Hagerstown MD SP
Blackwoods (Acadia) Bar Harbor ME NP
Winslow Memorial Park Freeport ME CP
Apgar West Glacier MT NP
Black Balsam Parking Lot Pisgah NC NF
Buzzard Road Waterville NC NF
Cataloochee GSMNP Waynesville NC NP
Crabtree Meadow Marion NC NP
Davidson River Brevard NC NF
Deep Creek Bryson City NC NP
Doughton Park Sparta NC NP
Hanging Rock Danbury NC SP
Harmon Den Waterville NC NF
Jordan Lake SRA (Poplar Point) Wilsonville NC SRA
Julian Price Blowing Rock NC NP
Lake Powhatan Asheville NC NF (few sites with power)
NC Fairgrounds Raleigh NC COM
Oregon Inlet Kitty Hawk NC NP
Pilot Mountain Pilot NC SP
Pisgah Brevard NC NF
Rocky Bluff Hot Springs NC NF
Smokemont GSMNP NC NP
Stone Mountain Roaring Gap NC SP
Pillsbury Washington NH SP
Sugar Loaf Twin City NH NF
Waterville Waterville NH NF
Wildwood Woodsville NH NF
Cranberry Lake Cranberry Lake NY SP
Lake Taghkanic Taghkanic NY SP
Woodland Valley Kingston NY SP
Congaree Hopkins SC NP
Francis Marion Awendaw SC BD
Kristina's Reeseville SC PR
Linville Falls Linville Falls SC NP
Parson Mountain Abbeyville SC NF
Abrahm Creek GSMNP TN NP
Big Ridge Maynardville TN SP
Breaks Interstate Park Haysi TN SP
Cades Cove GSMNP TN NP
Chilhowee Parksville TN NF
Cosby Cosby TN NP
Cumberland Gap Cumberland Gap TN NP
Elkmont GSMNP TN NP
Frozen Head Oliversrings TN SP
Meeman-Shelby Forest Millington TN SP
Thunder Rock Ducktown TN NF
South Washington UT NP
Bark Lake Norton VA NF
Bear Tree Damascus VA NF
Cromer's Rock Speedwell VA NF
High Knob Norton VA NF
Lewis Mountain Elkton VA NP
Mathew Arm Laura VA NP
Raven Cliff Speedwell VA NF
Rocky Knop Roanoke VA NP
White Rocks Pearisburg VA NF
Button Bay Vergennes VT SP
Little River Waterbury VT SP
Blue Bend Lewisburg WV NF
Grandview Sandbar New River gorge WV NP
Tea Creek Marlinton WV NF
Bridge Bay Yellowstone WY NP
2015 Ram 3500 4x4 Crew Cab SRW 6.4 Hemi LB 3.73 (12.4 hand calc avg mpg after 92,000 miles with camper)
2004 Lance 815 (prev: 2004 FW 35'; 1994 TT 30'; Tents)