Keep in mind that this game takes place in the middle of a desert and is far away from large population areas, unlike the east and west coast settings of the other games. It seems unlikely that the area would have been nuked directly.
On "The Vault" it's said that Cesar's Legions droped a nuke on "Camp Searchlight". That means that they had at least one nuke so why can't there be more than one.
I think that in Nevada should be more military installations especially because there isn't as much civil population as in other regions.