People interested in more than just the summit of Neighbor Mountain, which is just a 5-mile outing (RT) with little elevation change worth noting, may enjoy this loop that leads over Neighbor's summit and down to Jeremys Run, among Shenandoah National Park's prettiest streams. The route then climbs along Jeremys Run to reach the Appalachian Trail (AT), which leads back to the start.
Any time of the year is nice for this hike; spring will feature wildflowers and potentially interesting stream crossings, summer will tempt hikers to cool off in the pools and cascades of Jeremys Run, fall will delight with colorful foliage, and winter brings the best trail views and the possibility of spectacular snow and ice formations along the stream.
Most people will do this one as a day hike, but it would make a nice overnighter, too.
Locate a parking area less than half a mile south of the Jeremys Run Overlook on Skyline Drive. This is in the park's North District between Mileposts 26 and 27.
From the parking area, follow signpost directions for 0.2 miles along the AT to the Neighbor Mountain Trail, from which it is about 2.3 miles to the summit. About a mile before the summit, there are some rock formations with some interesting colors and textures on the right side of the trail. These formations are called the Gendarmes, and even though they're not challenging to scramble on, they make good photographic subjects, especially if you like closeups showing details.
From the summit, descend for 2.7 miles, sometimes steeply (elevation loss is about 1500'), to Jeremys Run Trail. Turn right and follow Jeremys Run upstream for 5.6 miles until you reach the AT, where you turn right and follow the AT for 3.3 miles back to the trailhead.
The Jeremys Run Trail involves 16 stream crossings. Much of the time, these crossings are ankle-deep or can be rock-hopped, but periods of heavy rain or snowmelt can make the crossings more difficult, even dangerous. Jeremys Run itself is a delightful series of pools, rapids, and small cascades. There are no major waterfalls on the stream, but it is beautiful nonetheless.
In all, this 14.1-mile hike involves about 1500' of elevation gain, more than half of it along the gentle-to-moderate grade up Jeremys Run.
I recommend waterproof boots for ankle protection on the steeper grades and for comfortable, safe stream crossings. Trekking poles are advisable to help with stream crossings.