Plan on Snow in Maine from middle of October to at least May1st. NMW is a working forest, privately owned by timber companies that allow recreational use of their property, for a fee. I've only been up there to camp once. The campsite we stayed at on Lake Umbazookus lake we shared with an older retired couple from Vermont that had the same campsite for the last 20 years for a few weeks in the Summer. It was quiet. We went to visit the ghost trains, pretty area. Talked to a couple couples canoeing the Northern Wilderness waterway. Avoid Black fly season iif you plan on spending any time outside. The season typically runs from Mother's day to the beginning of July. Mosquitoes start hatching from Father's day, and they seem to die off a bit by August and they don't go away until the nights start dipping below freezing, usually in October.
There is also Katahdin Woods and Waters National Monument to visit. Its not as large an area as the NMW, but has terrific views of Mt Katahdin.
Baxter state park is worth a trip, but its mostly geared towards hikers. We did drive through the park a couple times this year to avoid the paved roads. Pick a rainy day, not so much dust kicked up on the tote road.
Buy a Maine Gazeteer. 80% of Maine is privately owned, but Maine has a long history and tradition of allowing public access on private land. The Gazeteer will show you logging roads and paved roads you can travel on. Most roads in Maine go North and South to follow the old railways that were used to haul timber down to Portland and Boston. Typically,any roads going east and west will be dirt.
I'd avoid the auto road to Mt Washington on a weekend, unless you want to stay stuck in a line for hours. I find it more enjoyable to walk up the mountain, but I'm a hiker. Its what I do.
The White Mountain National Forest has free camping in a few places along forest roads. I've never used any of the sites, but they look nice, for primitive camping.
Acadia is worth a visit, but once again, avoid the weekends. I avoid Acadia in the Summer. Too many people, too much traffic. I usually go for a week in the fall, after the tourists are gone and before the park is officially shut down for the season. Its cooler, the fall foliage is brilliant and the hiking trails aren't crowded.
Western Maine is less wild than Northern Maine, but still lots of areas to explore. Coastal Maine is built up and almost unbroken tourist trap. I avoid Rt1 almost all Summer, except for this year. Drove up to Ft Kent on Rt1 on memorial weekend and barely any traffic. Of course, nothing was open due to our crazy governor shutting everything down and tanking the economy out of fear of Covid. Now, its 100 times worse than it was 6 months ago.
For those that may care, Constitutional Carry is the law in Maine. Weed is legal, but having a firearm and in possession of weed is still a federal offense. Keep that in mind.