Goldmyer hot spring via National Forest Development Road 5620 Trail(edit)

At the end of a long gradual hill, the old roadbed widens into an open area roughly 25' in diameter(large enough to fit two or three Semi-trucks with trailers).  There will be a fork in the road and a sign high in the tree for Goldmyer. Follow the fork to the right heading downhill. A very short distance later, you will cross the Middle Fork River on a footbridge.  Once across the bridge, immediately turn right onto the Middle Fork trail.  A very short distance later turn left at the intersection. 1/4 mile later you will arrive at the Caretaker's Cabin (you will see a green welcome sign prior to reaching the cabin).  Please ring the bell on the welcome sign and check in with the caretakers upon arrival. Also ring bell to check out.

Not actually that long. Probably about 4.5 miles each way. This is from the trailhead at the end of the Middle Fork Rd to the caretaker's cabin. Get reservations and enjoy, it's very worth the trouble of jumping through the conservation hoops.

https://connect.garmin.com/modern/activity/19244608027