I'm in Lynchburg, VA, so everything I do is in the Central VA section of the trail.
Ramsey's Draft is a good area, but a little short for 3-4 nights. Some places to look at.
Grayson Highlands in the southern part of VA has a whole bunch of trails that you can make a really good loop out of. Mount Rogers is there, and that's the highest point in VA. Cool place.
My favorite section of the trail is right by Roanoke, the area from Dragons Tooth to Tinker Cliffs is awesome. There's an outdoor store right by the trailhead in Troutville called Outdoor Trails, you can park your car in their parking lot, and pay about $30 for a hiker shuttle to the Dragons Tooth parking lot, and then hike back to your car NOBO on the AT. I think it's 27 or 30 Miles total. Only issue is water is slightly scarce on that section of the trail, and the creek at Lambert's Meadow shelter is confirmed to have giardia in it.
I've hiked the section from VA 60 up to Reed's Gap, it's fun, but full of hills. If you go from the 60 parking lot to Dripping Rock on the Blue Ridge Parkway, you're looking at 43 miles. Only downside is there's no way to make it a loop, so you'll need to either do an out-and-back, or bring two vehicles. But it's an awesome hike. Be prepared to hike though. It's got something like 12,000 feet of elevation gain/loss.
Other places to look:
The VA 501 trailhead is nice and accessible, but not matter which way you go, you're going up, since it sits in a river valley. Going NOBO you hit Big Rocky Row, and the Punchbowl, which is cool, going SOBO you get to Pettits Gap and Apple Orchard Falls.
If you're looking for a loop, go to Grayson. If you're ok with paying for a shuttle, go do Tinker/Macafee, because I'll say it's the best section of trail in VA.