The Cheyenne mountain complex was designed to withstand up to a 30 megaton blast within 1-nautical-mile.
I doubt that any, declassified (or circa 1970) facility could with stand a direct hit, just because the blast pressures rise exponentially the closer the facility is to ground zero. Although, in the early years of ICBM's accuracy wasnt really critical because of the wide diameter of distruction, so the odds were fairly good that a missile aimed at the complex would miss by a mile or more.
From a technical standpoint, a direct hit on the cheyenne complex would be particularly bad, because it would defeat their first defense against the effects of a nuclear blast: the tunnel through the mountain that would allow the pressures from a side blast to leave the other side, rather than collect on the 25 tonn steel blast door. A perfectly targeted blast would cause extreme negative pressures within the tunnel, followed by extreme positive pressures as the evacuated air rushes back in. These would concentrate on the blast door and more than likely lead to the distruction of the facility.
@cp_scipi
You watch quite a few scifi movies, dont ya?
A nuclear blast does not vaporize everything in a huge fireball....well, it does make a fireball and it does destroy everything, but it will not vaporize a mountain. A facility such as the cheyenne complex actually has little to fear from the "nuclear fireball",as they are well shielded by up to 200ft of earth and reinforced concrete. Their biggest enemy is the pressure waves that both precede and follow a nuclear detonation. Look back at the common footage from the 1950's nuclear tests. You will notice that first the test houses burst into flames, then they are blown apart one way and then the other. The fire may be damaging, but it would have little effect on a reinforced concrete structure without the associated pressure waves.
As for the radioactive lava, during the tests in the 50's, scientists did report that the sand floor of the test bed had collected a layer of glass, but that was in an extremely small radius around ground zero. I would hardly call that "converted to radioactive lava".