*** SPOILERS ***
According to in-game lore, 77 nukes fell on the Vegas area. Defenses put in place by a private (and extremely rich) citizen took out over sixty of them, sparing the Hoover Dam and urban Vegas itself. The rest impacted around the area, hitting Nellis AFB and such, and the resulting fallout killed most of the inhabitants. Not to mention more fallout which would have blown in from the West Coast on the prevailing winds...
By 2781, the radiation at Nellis, at least, has cleared. There are some areas still radioactive, but mostly it's a clean wasteland. And take it from someone who lives in the Desert Southwest? Yeah. That's what it generally looks like out there.
FYI, radiation in the Fallout universe is already known to behave differently from real life, turning people into Ghouls and somehow preserving non-living matter. So blasted clapboard houses and Salisbury Steak TV dinners don't turn to dust as they should, but remain (relatively) inhabitable and edible, respectively.