(I specified American because the Soviets and Russians have historically lagged behind here, and it looks like that's still the case. I don't know what the story is for other ICBM-equipped powers. The Soviets compensated for their lesser accuracy by fielding larger bombs.)
Also keep in mind that the major factor limiting ICBM accuracy these days is the need to be completely self contained, since they're intended to operate in the middle of World War III, and no external navigation sources can be counted on. Slap a JDAM guidance system on the warhead and your ICBM can deliver it to within whatever square meter you're most interested in.
ICBMs armed with conventional bombs have been considered, since accuracy can be enough for that to work now. As far as I know, the only reasons these haven't been deployed are cost (using up an entire ICBM to deliver a chemical bomb seems wasteful) and, probably more importantly, the fact that there's no way to tell whether a given ICBM is carrying a nuclear warhead or not, thus the strong possibility that using such a weapon could trigger a nuclear war by accident. See:
The CEP figure represents the radius of a circle where there is a 50% chance of the bomb landing within that circle. The CEP figure is basically 2/3 of a standard deviation.
In any case, accuracy is gated by navigational accuracy, not so much guidance, as long as your initial aim isn't too bad. ICBMs have a 100m CEP because they're using inertial navigation all the way. Switch to GPS and you'll have no trouble doing better. In the context of SpaceX, getting the rocket to within a few hundred meters of the landing pad is perfectly fine initially, because it can then maneuver to the pad more precisely.