I can get you to Red Rock. Take Charleston (turns into Blue Diamond road?) west out of town until you get to Red Rock Canyon State Park. Park somewhere near the visitor's center and go up the road that goes off the the right from Charleston / Blue Diamond Road. In all, it is a 13 mile loop, all up for the first 4 miles, and then up and down back to the highway, where you turn left to get back to the visitor's center and start another lap.
I have heard that the climb up to the end of the road (Lee Canyon) from U.S. 95 (?) up Mount Charleston is very good, but I haven't done it. Valley of Fire State Park and the portion of the road around Lake Mead that is near the park are also supposed to be good.