I think it might be safe-ish to assume that one of the things that might have made WW3 actually happen is the reduction of MAD as deterrent concept. Either ABM technology or arms reductions had gone to the point where the great powers no longer felt threatened by assured destruction. The fact that so many major population centers survived suggests that the gigantic stockpiles of multi-megaton MIRV warheads were no longer a valid counterforce weapon. If there was a nuclear exchange, the first shots with the really big warheads (e.g. Minuteman III silos) would probably be aimed at counterforce operations and the hits on cities would probably be single SLBMs from the surviving ballistic missile subs. Also the recent wave of arms reduction treaties have reduced the total stockpiles and put restrictions on things like delivery systems.
So we can probably see half of lower Manhattan being destroyed by a ~100-250kt SLBM, but there's probably sufficient defenses to keep that from outright destroying the city.
The thing that's more likely to cause long-term damage to things like governance is the destruction of electronics stemming from widespread EMP. Again, as postulated earlier, if ABM systems are sufficiently advanced, they may have gone for targetting high altitude bursts with the goal of knocking out the entire communications infrastructure of modern states instead of killing people (perhaps expecting limited retaliation as a result).
Either way, we're probably not talking about a Cuban Missile Crisis retaliation style outcome, but more an outcome where you have cities badly damaged, but not rendered completely uninhabitable by the nuclear exchange.