Vic,
If your preference to remote approaches an aversion to crowds, much of the US part of the Appalachians during leaf season may not be for you.
That said, some ideas to consider would be:
Pass through New England to emerge in mid-upstate eastern NY and cross west into PA well wide of the NYC area (like 100 to 150 miles wide of it!). The actual site of the Woodstock festival is at Bethel, NY and is pretty cool to see for some of us. It's a nice bushwhack south of Bethel into PA through hardwood forests most of the way. US 209 along the Delaware River and Delaware Water Gap Nat Rec area is pretty nice (though pretty close to NYC/Newark, etc), as are any routes west of there through central PA's Pocono Mountains.
A little closer to me (Raleigh, NC) is the Blue Ridge, Shenandoah Valley, and the Alleghany Mountains of northern/west-central VA. Shenandoah National Park (NP) lies atop the Blue Ridge immediately south of I-66 in northern VA and Skyline Drive runs its length for 105 miles down to Rockfish Gap, where Shenandoah NP ends and the Blue Ridge Parkway (BRP) begins. The BRP then runs 469 miles to Cherokee, NC, generally atop the Blue Ridge Mountains all the way. Some think 574 twisty, slow miles, most if not all of it fully choked with leaf season traffic is too much of a good thing. I am one of those people. But a drive parallel to I-81 through the 200 mile long Shenandoah Valley (the Valley) can be great. Massanutten Mountain is a 60 mile long sandstone ridge in the middle of the Valley and is within National Forest (NF) lands for both disbursed and campground (CG) camping. On the west side of the 30 mile wide Valley are the Alleghanies, also mostly within NF lands. Ridgetop driving and disbursed camping can be had west of Harrisonburg, VA at Reddish Knob and Flagpole Knob. South of there in the Alleghanies are Warm Springs and Hot Springs, VA, well within the "fold belt" of the Alleghanies simply meaning the terrain is long sandstone ridges (like dozens and dozens of miles) and long pastoral limestone valleys in between. Much of the ridge lands are NF lands. At Warm Springs, VA are the Jefferson Pools, where emanates one of only two natural hot springs in the Eastern US. Hidden Valley NF CG is around 5 miles west of there and is a rather secluded NF CG with miles of hiking trails along ridges and along the Jackson River.
Further south and on the east side of I-81 the BRP starts to pick up elevations of over 4,000' (ultimately reaching nearly 7,000' at Mount Mitchell, NC) and the width of the Blue Ridge Mountains rises from 10-12 miles out to, ultimately, +50 miles. Fun places to visit include Damascus, VA, where a rails-to-trails bike path called the Virginia Creeper Trail makes for a fine Autumn ride, but only Monday-Thursday, as weekend crowds are thick. The eastern half of the VCT is 17 miles all downhill from Whitetop Station back to Damascus, so the normal trip is to rent bikes and pay for a shuttle in Damascus, be driven 30 minutes up to Whitetop, and gently cruise 2.5-3.0 hours back to Damascus. Around 1/3 of the route is along nice mountain streams and it's pretty much all within NF lands composed of unbroken hardwood forest. Around $30/pp gets you a nice Trek fat tire comfort cruiser and the shuttle up the mountain--a great deal.
I'd recommend Boone and Blowing Rock, NC but proximity to the densely populated NC Piedmont means Autumn weekends and even weekday crowds along the BRP can take a lot of the fun away. But, Julian Price Memorial Park CG and Grandfather Mountain State Park's backcountry trails, each just south on the BRP from Blowing Rock, stand out as places worthy of a mid-week shot. A nice 3.5 mile trail from Milepost 300 gains 2,000' to Calloway Peak (the highest of the 5 peaks making up Grandfather Mountain) at just under 6,000' and features 100 mile views on a clear day.
South of there and on the far western edge of the Blue Ridge Mountains is Erwin, TN, where the Appalachian Trail (AT) crosses the Nolichucky River. Lots of good section-hiking along the AT, including the Roan Balds, a stretch of a dozen miles largely treeless up top and holding elevations between 5,000' and 6,300' . Paddling the Nolichucky can be a lot of fun and the take-out is right by the AT outside of Erwin. A nice riverside commercial CG close to the take-out provides opportunity to get out of the river and get dry and warm without a long bus ride back to town.
Further south and back in the middle of the Blue Ridge is Hot Springs, NC, home of the second natural hot springs in the East. The AT goes right through town, as does the French Broad River, so there's a nonstop hiking/single-track/paddling vibe. Hot Springs is pretty much surrounded by NF lands with lots of off-highway graded gravel road driving and practically unlimited disbursed camping, plus a goodly selection of NF CGs. The Hot Springs Resort owns the Springs and the large riverside CG. Each are a bit spendy but being right at the edge of town, thus walking distance to lots of fun restaurants and bars, has its advantages. The hot springs are piped into about a dozen Jacuzzi-style tubs, each fully privacy screened with one open side facing the French Broad River or Springs Creek. Also spendy at around $30/hour, but a fine way to relax from hiking/paddling/driving all day. And the springs are BYOB, if you like that kind of thing.
Similar to my reservations about Boone-Blowing Rock, I can't in good faith recommend visiting the Great Smoky Mountains NP in Autumn. It's the most-visited NP of all and it's basically wall-to-wall cars and RVs during October's leaf season. I wouldn't go there then if you paid me to.
In general, the colors of course start in the north and travel south. But beware of the significant effect which elevation has on the timing of peak colors. For example, elevations between 4,000' and 6,000' in the Blue Ridge will peak within a few days to a week of October 15. At the same latitude, but down at around 1,000'-2,000', peak won't be before the 3rd-4th week in October. I would guess peak colors in the Green Mountains and White Mountains in Vermont and New Hampshire would be the very last part of September/very earliest part of October but that lower elevation parts of New England would be more like the Blue Ridge's mid-October peak. Bottom line is to just be aware that peak in lower elevation parts of New England is happening more-or-less simultaneously with peak at higher elevations about 1,000 miles to the south.
Sounds like a fine plan is simmering. Please don't tell my wife, lest she insist on the same thing!
Foy