"Best" range near Vegas. Best is pretty subjective. If you are looking for a public 1,000 yard range the answer is there isn't one.
The Clark County Range up by the Air force base is not yet open;
Desert Sportsman (in Red Rock) only goes to 600 meters, and I recall it is member only (or invited guest);
Boulder Rifle and Pistol Club has the only 1,000 yard range in Southern Nevada (there may be one up near Reno - but I'm not sure about that). The 1,000 yard range at Boulder is only used part of the time (as in for NRA matches and scheduled practices), as it requires closure of the rest of the memeber ranges. The member range also has a steel target range that has steel starting at 110 yards out to 866. The public portion of Boulder has several 100 yard ranges, but taht is it other than pistol pits.
JeffVN