Even though Vegas and the surrounding area was virtually untouched by bombs... I guess it took a few hours for the radiation to waft over and break all the clocks..
But... but... it's the electromagnetic disruption of a nuclear blast that stops clocks. In Vegas they should all show different times depending upon when the batteries ran out, or for ones operating on the mains, when the power station failed - which would vary depending upon type of power station.
Yes I know I'm just being pedantic at this point