Most likely it's a myth.
First, nothing is "outside of ICBM range".
The so-called "closed cities" were primarily nuclear production or research sites.1 They were presumably on the primary hit list and were hardly a "safe haven" in case of a nuclear war. In peacetime though living there was a privilege as the supply standards were (much) higher than elsewhere.2 But this was hardly a concern for "children of the high ranking people".
If such "safe haven" city existed, it would surely be known and would be added to the hit list.
Moscow was the only city (with surroundings) protected by the anti-ICBM system. So it was probably the safer place to be (of the cities with acceptable living standards for such people).
Personally, after living in the USSR (and in a "closed city"), I've never heard of such arrangement. Everyone wanted to be in Moscow.
Surely, emergency evacuation plans existed. But the situation was never dire enough (after the early 60s at least) to start evacuating children preemptively.
1 Not to be confused with many border cities or larger industrial cities were foreigners were not admitted. They often went under the same moniker of a "closed city". But the dozen or so "real ones" were closed even for Soviet citizens. They usually had code names and were not even shown on maps.
2 Except perhaps Moscow, another very privileged city with restricted access (for migration).