UPDATE: The monument site was renovated in 2016. I visited it last week and have posted a new blog entry here about the new site.
On my latest return from Zion NP, I drove to the corner where Utah and Arizona butt up against Nevada. My map labeled the place as "Initial Monument." I'd never heard of that before. A lot of googling found some posts by adventurous people who'd visited the site. They reported that it required 4wd and they had to hike the last stretch. They also indicated that a geocache was located there. This sounded like a challenge to me. Here's a google map centered on the location. Google Earth already shows somebody's Panoramio photo of the site.
I used google maps satellite images to choose my route, a mere 17 miles off interstate I-15 from Littlefield. Almost all of those roads were passable by any vehicle. A few of which I could drive at 40 mph. The last few miles were on a ranch road along their barbwire fence. That was the funnest part of the drive, and does require high clearance (but not necessarily 4wd) to go through some fun (sharp) drops of about 6 feet into 6 ft washes then right back up.
The monument is marked with a 3 ft tall sandstone monolith. I found a source on the web that said this monument was placed there in 1901. The states are engraved into the sandstone on each side. One side reads "NL 37" indicating that this monument is at 37 deg north latitude, which is the latitude of the border between Utah and Arizona.
I took a photo of my Garmin display while I was there, as well as photos of the geocache contents. It was windy and overcast and still 102F. Nicer than the 117F down at Littlefield.
Lastly, here's a map indicating my route for anybody who's interested in a brief diversion from their drive along I-15.
UPDATE: I've received a request for more details about the route, so I'm attaching a few more annotated Google maps. Most of the route is a wide graded dirt road where you can drive 35+ mph. That's why it doesn't take very long to get to the end. As I mentioned in the comments, the last stretch of road is not graded, it is less used and follows a fence line. That road crosses a few (2 or 3) gullies that might cause problems if you have bad approach/departure angles. But you can always stop and hike from there - it's not very far.
The only place you might get a little lost, is in the area of the orange path. I missed the right turn and then went on to the corner (orange path) and turned there. The green circles mark the gullies. I hope my description isn't out of date. I plan to drive the route again in the next couple months just to see if the route is still as easy as it was in 2009.