This might be an unpopular opinion. But if you need motorized conveyance to camp remotely... then you should probably not camp remotely. It's ok if some wild areas are less accessible.
Seriously, we have nothing over here. All the land was bought up, often before there even was a united states. And the forests we do have tend to be very heavily regulated. You want to do anything it's all pay for permit and be clustered with a bunch of other permit buyers.
I am not aware of single forest in the Northeast where you can just drive in, camp, and leave without breaking the law.
I've done exactly what you describe (drive in, camp, leave without breaking the law) in the White Mountains in NH[0].
In general, dispersed camping[1] is legal in almost all national forest and BLM land. I think many people don't realize this but you can camp for free almost anywhere in a national forest (keeping certain distances from trails, roads and bodies of water)
If you hike in you can camp on the east coast, generally you must be at least 1/4 mile from where you park. On the west coats you can just pull in with your car and set up camp right there.
Historically, Maine had excellent recreation policies in cooperation with the private paper companies that owned the majority of land in the northern part of the state: areas not actively being logged were available for recreation access, as were vehicles on logging roads (though you best yield to the logging trucks that drive down the middle of the roads, even if it means you need to dive into the ditch). State recreation fees for snowmobiles, fishing, etc. would cover things like insuring the private landowners against liability.
However, starting in the mid/late 90's, much of the paper company land was divested and sold to private equity land holders (yay modern finance!) and those previous open access policies have been very much curtailed. It's a big loss to the community, but it sure must be making some money for shareholders somewhere...
There's lots of state + national forest land in the Northeast where that's legal. I've done it many times in PA/NY/VT/NH/ME. There are probably some options in the other more developed states too, but I don't usually visit them as much for outdoor recreation.
Outside of the most popular locations for tourists that's pretty much the default.
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If you've had trouble finding this, have you been limiting your search to parks? Parks are usually more heavily restricted in terms of camping.
In NY, the state parks will be heavily regulated having designated pay for/reserved camp spots along with amenities. However, the forest preserves (Adirondacks/Catskills) and state forests do allow backcountry/primitive camping.
Just look for a nearby state forest and look up the dec regulations for that site. More than likely you can can primitive camp there.
I've done it, it's just a huge PIA compared to out west where you just get on forest roads where there are clearings you pull into an camp all over the place.
The east coast just has this strong hostility towards camping for some reason.
There are a lot more people looking to camp in generally smaller areas especially on weekends. And the east doesn’t have the large networks of forest roads and almost roads and not really roads that you have in many western national forests and BLM land.
The West obviously has plenty of camping restrictions in popular areas like national parks and wilderness areas where you may have year in advance lotteries.
I’m not sure why the east would be uniquely hostile given the same agencies administer federal land across the whole country.
But, in general, yes if you want to get away from people and have more flexibility in where you can camp, you’re probably best off traveling to the western states.
There is comparatively very little federal land on the east coast. And even where there is land, it's not as friendly as the west.
Using white mountain NF as an example, their camping policy is much more restrictive than western national forests (i.e camp away from roads and trails).
There is virtually no BLM land and national parks are kinda strict all over. So you are left with state land and they tend to like structured campgrounds that you pay buy permits for.
White Mountain National Forest for one. There are restriction regarding how close to a trail or hut you can camp and the topography can be challenging but you certainly can.
But yes there are orders of magnitude more national forest
land out west. Probably more than the size of the entire or maybe UK.
Check out the White Mountain National Forest in New Hampshire or the Green Mountain National Forest in Vermont. I've heard it's also legal in CT State Forests but haven't actually seen this written down anywhere.
Which can also make camping and hiking in those areas far more dangerous. If a rescue team have hike in 20 miles to get you without any motorized vehicles and can't get a chopper into those remote areas? They shouldn't be remote, they should just be left completely inaccessible.
The problem then is people these days, IMHO are far more reckless and stupid and will try and prove Mother Nature wrong by attempting to go into these areas to get internet cred from Tik Tok and other platforms. Perfect example is the people who go to Longs Peak and attempt the Keyhole Route thinking its a well traveled hike and easy.
It's okay for some areas and activities to be more dangerous. "Completely inaccessible" is banning access for safetyism.
Decades of deaths in activities like backcountry skiing staying relatively flat while the numbers of people doing those activities exploding would go directly against your assertion that people are more reckless and stupid in the social media age than they were in the past.
If things like the Keyhole route are outside of your risk tolerance, that's a perfectly valid and rational decision. I'd encourage you not to do them. That doesn't mean no one else should be allowed to take risks you don't.