The range is Desert Sportsman Rifle and Pistol Club (DSRPC) in Las Vegas located on Hwy 159 / Charleston Blvd toward Red Rocks just a mile out of town. The membership fee is very affordable ($200 year and less if you are 60 or older) plus you have to take a two hour range orientation.
Desert Sportsman's Rifle & Pistol Club
There's a very active long range shooting group out there as well as competitions put on by locals on the Nevada Shooters forum.
I know there's a 650 yard range and multiple 400 yard ranges. I believe there was or still is a 1000 yard berm but it is closed. Don't quote me but I know it's not open anymore. My assumption is 650 yard is child's play for the experienced shooters here but until I get there it's a long distance.