Well, Wheeler pass is a staple. You drive up to Cold Creek (North from Las Vegas on US95, just before you come to Indian Springs); you turn right at the Indian Springs prison. Drive out that road toward the Cold Creek community. Before reaching Cold Creek itself you come to a fork in the road; I believe there is a falling down concrete building there. Keep to the left, the right fork takes you to the houses at Cold Creek. You will go through a creek. On the other side you should see where other people have continued on up the hill. If you continue up the hill, you will drive over the mountain and eventually come out in Pahrump.
Mt. Potesi: Drive down I:15 to Jean. Exit at Jean and turn right. Continue on to the little town out there (I don't remember what it is called. Off to the right, behind the houses are numerous dirt roads. Through trial and error, you will find one that takes you up the mountain. The road is steep and rough. But, you will go up to somewhere around 12,000 feet.
Another staple is Lovel Canyon road. Drive out highway 160 toward Pahrump. You cross over the mountain and start down the other side. You will come to a road off to the right that has a sign saying Lovel Canyon. Turn there. This is a relatively short trip that will take you through some nice scenery. Keep to the left as you drive up the road. The dirt road will go up in the mountains and come down back on HWY 160 through Carpenter Canyon. There is some way on this road to come out at Red Rock Canyon, but I don't know where it is.
This should give you a few weekends of fun. I can give you more as time goes on. Of course every one of these roads has countless other roads off the main road to explore. The high altitude roads are great on the summer to get out of the heat. It is still hot, but not super hot.