Take the Brigham City exit, and head East through and past the city. Drive through this canyon a bit, and the first town you should come across is Mantua. Turn East into Mantua, and once you hit Main Street, turn right. Main will peter out to the South and turns into gravel towards the mountains. I have a VW Beetle, and I had to stop a few miles up this road when it turned just too rough. I mountain biked the rest. I would guess any high clearance vehicle could make this road.
The road will eventually crest and decend into Willard Basin.
A little more about this route. After exiting I-15 at exit 364 for Brigham City proceed on East Hwy. 91 for a little over 5 miles and take the Mantua exit. At the first stop sign you're at a "T" and should turn right onto Main St.; zero your odometer here. About a 1/2 mile later you'll see a sign for Willard Basin (11 miles) and Inspiration Point (13 miles). The pavement ends at 1.6 miles and you'll come upon the Dock Flat campground at ~ 2.5 miles. Unless you're in a 4X4 or other high-clearance vehicle this is a good place to stop. Continuing on the dirt road to ~ 7 - 7.1 miles you'll reach a saddle with plenty of parking. The road to the Willard Basin campground and further to Inspiration Point continues to the left and south from the saddle but could only be traveled ~ 1 mile when I was there 7/1/09 due to snow and trees blocking the way.