Recently took a day trip to Picacho State Recreation Area. Entered through the Picacho Wash area. Right on the California/Arizona border. Wish I had more time to stay the night. Will definitely return. Good camping spots about 25 miles in, along the Colorado River. Trail was pretty easy. Stayed in 2WD the whole time. You can also approach the area from the West via the Indian Pass Road off S34. It was a perfect day for trail riding and plinking.
Nevada is a beautiful state, with large amounts of BLM land, which means if you find a spot to camp off the main road, you can use it.
Middle of NV is a great little campground called Bob Scott Campground. Good for an overnight, and it's on hwy 50, which has all sorts of historical markers and neat looking dirt off shoots, as well as dramatic panoramic views. Taking a week to explore this portion of the highway (in NV) is surely worth the trip itself.
At the eastern end of NV there is a beautiful little hot springs that isn't hugely known, is a bit off the beaten path, and is a local favorite. I didn't notice if there were "No Camping" signs around, but I intend to find out. I intentionally did not give coordinates, because it is searchable and there are good reviews that will help you get there. Worth the adventure.