Question: Where is most of the mountain contained that is the highest natural point in the Commonwealth of Virginia and also immediately east of the second highest named summit in Virginia?

Context paragraphs:
Sand Hill (Noble County, Indiana): Sand Hill (1070+ feet or 326+ m) is the second highest named summit in the U.S. state of Indiana.  It is located in northeastern Wayne Township in Noble County, approximately two and a half miles southeast of the town of South Milford.  A burial ground known as Weston Chapel Cemetery is on the southeastern face of the hill.

Mount Rogers: Mount Rogers is the highest natural point in the Commonwealth of Virginia, United States, with a summit elevation of 5729 ft above mean sea level.  The summit straddles the border of Grayson and Smyth Counties, Virginia, about 6.45 mi WSW of Troutdale, Virginia.  Most of the mountain is contained within the Lewis Fork Wilderness, while the entire area is part of the Mount Rogers National Recreation Area, which itself is a part of the Jefferson National Forest.

Cheriton Hill: Cheriton Hill is a hill overlooking the English Channel near Folkestone in the south-east corner of Kent, England.  The relatively low-lying hill (reaching only 188 metres above sea level) is covered with farmland, villages, narrow lanes, and footpaths.  The highest point is on a covered reservoir next to the trig point; the highest natural point is nearby, probably close to the road to the village of Paddlesworth, near a transmitter mast, but the relatively flat summit gives no real impression of being on top of a hill.

Yding Skovhøj: Yding Skovhøj in Horsens municipality, Jutland is one of Denmark's highest points.  Its height is 172.54 m above sea level when the height of one of the Bronze Age burial mounds built on the top of the hill is included.  If these man-made structures are ignored the hill's highest point is at 170.77 m, which is 9 cm lower than Denmark's highest natural point, Møllehøj at 170.86 m. Ejer Bavnehøj is Denmark's third highest natural point at 170.35 m.

Pine Mountain (Grayson County, Virginia): Pine Mountain is a mountain in the Blue Ridge Mountains.  It is located in the Mount Rogers National Recreation Area of the Jefferson National Forest, within Grayson County, Virginia, United States.  The peak is immediately east of the highest mountain of Virginia, Mount Rogers, and Pine Mountain's sparsely vegetated summit has excellent views of both Mount Rogers and the surrounding region.  The Appalachian Trail passes within feet of the summit.  Pine Mountain is the second highest named summit in Virginia, though because its topographic prominence is well under 300 feet, it is considered a subsidiary peak of Mount Rogers.

Hoye-Crest: Hoye-Crest is a summit along Backbone Mountain just inside of Garrett County, Maryland, USA.  It is the highest natural point in Maryland at an elevation of 3360 ft .

Mount Arvon: Mount Arvon, elevation 1,979 ft , located in L'Anse Township, Baraga County, is the highest natural point in the U.S. state of Michigan.  Like nearby Arvon Township, Mount Arvon takes its name from the deposits of slate in the area which were reminiscent of those around Caernarfon in Wales.  Mount Arvon is part of the Huron Mountains.  It rises about 8 mi south of Lake Superior (elevation 591 ft ).  On the list of highest natural points in each U.S. state, Mount Arvon ranks 38th.

Mount Greylock: Mount Greylock is the highest natural point in Massachusetts at 3489 ft .  Its peak is located in the northwest corner of the state in the western part of the town of Adams (near its border with Williamstown) in Berkshire County.  Although geologically part of the Taconic Mountains, Mount Greylock is commonly associated with the abutting Berkshire Hills to the east.  The mountain is known for its expansive views encompassing five states and the only taiga-boreal forest in the state.  A seasonal automobile road (open annually from late May through November 1) climbs to the summit, where stands the iconic 93 ft lighthouse-like Massachusetts Veterans War Memorial Tower.  A network of hiking trails traverse the mountain, including the 2179 mi Appalachian Trail.  Mount Greylock State Reservation was created in 1898 as Massachusetts' first public land for the purpose of forest preservation.

Mount Walter (New Mexico): Mount Walter is the second highest named summit in the U.S. state of New Mexico, rising to 13,141 feet above sea level.  However it is not usually counted as an independent mountain since it has only about 53 ft of topographic prominence, and is only 0.4 mi north-northeast of Wheeler Peak, the highest peak in New Mexico.  Both peaks lie in the Taos Mountains, a subrange of the Sangre de Cristo Mountains, which is in turn a subrange of the Rocky Mountains.  They are also in the Wheeler Peak Wilderness of Carson National Forest.

Black Elk Peak: Black Elk Peak (formerly Harney Peak) is the highest natural point in South Dakota.  It lies in the Black Elk Wilderness area, in southern Pennington County, in the Black Hills National Forest.  The peak lies 3.7 mi west-southwest of Mount Rushmore.  At 7242 ft , it has been described by the Board on Geographical Names as the highest summit in the United States east of the Rocky Mountains.  It is also known as Hinhan Kaga (in Lakota).

Supporting paragraphs: Pine Mountain (Grayson County, Virginia) Mount Rogers
Answer: Lewis Fork Wilderness