Now to find some of the National Parks that have said high clearance 4x4 roads. I tried searching for "high clearance" within nps.gov itself, but this probably misses some here and there. I know for a fact that Canyonlands and Capitol Reef NPs and Guadalupe Mountains Natl Monument have such roads, having either driven them in the past or considered driving them and deciding that it wasn't a prudent idea at the time, and utah.com turned out to have sections dedicated to them.
Here's an alphabetical list that likely is far from comprehensive, and, again, is only covering National Parks save for the Route 66 bit (which I found as it was hosted on nps.gov):
Arches National Park, and the surrounding Moab area: Arches and Moab are chock-full of off road goodness. Slickrock isn't just for bicycles! Without going full-retard rock crawler there are many places that are most easily accessed in Arches with a 4x4:
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Big Bend National Park, Primitive Dirt Roads: There are 4 unimproved dirt roads in Big Bend NP totaling 101.5 miles, as well as many more miles of improved dirt roads with variable conditions.
Capitol Reef National Park: There are over 100 miles of unmaintained roads, with ditches and the occasional stream crossing, within Capitol Reef. I did the Cathedral Valley loop in 2003, a 58-mile off-road journey that mostly was within the capability of, say, a Subaru Forester (I indeed saw one) but which had segments that truly did require low range and better clearance/approach/departure angles. See the first photo in the above post for one vista from the Cathedral Valley loop. The Temples of the Sun (foreground) and the Moon (background) are below, also from that same loop:
Canyonlands National Park, Shafer Rim Trail and others: Canyonlands "is one of the world's great places for off-road adventure" per utah.com. After seeing the below photo from the Shafer Rim road that leads to the 100 mile White Rim Trail I wouldn't disagree. Some of the descriptions lead me to pucker up a bit, and indeed I declined to go off-road when I visited Canyonlands for (justified) fear of not being prepared enough. This is a place where a sat phone, a few buddies, shovels, traction aids to free oneself from sand, proper tires, and plenty of gas and supplies would be a Good Idea (tm).
Death Valley National Park, Unmaintained Dirt or 4WD Roads: There are at least several hundred miles of high clearance +/- 4x4 roads in and near Death Valley NP listed at the link. There are also many dozens if not hundreds or more miles of
maintained dirt roads and
roads outside the national park's boundary. There's also a
nicer PDF that the Park Service threw together that apparently highlights some of the better (?) unmaintained roads. Somewhat ominously, several of the descriptions for the unmaintained roads stress that only
short wheelbase high clearance 4x4 vehicles the size of a Jeep Wrangler are recommended. Yikes. Check out this declaration, for instance:
High clearance 4WD with short-wheel base beyond Lee’s Camp to upper Echo Canyon (CCJ-5 or smaller). Even the best drivers may do some damage going over the dry fall. There is one section that is so tight that a small 4WD can barely get through. Travel along this old road is not recommended unless part of a vehicle caravan. Rangers cannot reach you if help is needed.
El Malpais National Monument: Although there are two main roads accessible by all vehicles, all the other roads at this national monument are of the high clearance 4x4-recommended variety.
Great Sand Dunes National Park and Preserve, trail access and Medano Pass 4WD Road: There are a few optional hiking trail access points only accessible via high clearance 4x4 vehicle, and the Medano Pass road, with stream crossings and the like, is restricted to 4x4s. I didn't go to Great Sand Dunes on my 2003 roadtrip, but instead visited
White Sand National Monument where I shot a few vistas such as this one:
Guadalupe Mountains National Park, Williams Ranch: 7.3 miles out and then the same back to access a historic ranchhouse up in the mountains. I did this one as part of my 2003 roadtrip (see photo above with front fender of purple Pathfinder in view, and this resulting underwhelming photo at the ranchhouse itself):
Mount Logan Wilderness Area: Although Wilderness Areas themselves forbid any mechanized transport, including bicycles, let alone a clanking 4x4, the Mount Logan Wilderness Area just north of the Colorado River near the Grand Canyon actually requires a 2.5 hr drive on a high clearance vehicle-only dirt road just to reach its boundary!
Route 66 as it crosses New Mexico: Trying to follow the path of historic Route 66 can require traversing unmaintained stretches that are only suitable for high-clearance vehicles now.
