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It would not be hard to smuggle them into a large city.
Well, actually, it might be. It may or may not still be classified, but it is not a secret that the US has nuclear emission detectors that can be used to detect the presence of a bomb from several miles away. You do have to aim it right in the direction of the device, but...you can detect whether an aircraft or a ship is carrying such a device.
Now someone who knows this can shield the device by surrounding it with enough water or lead. However, it is then essentially difficult to sneak it to the target. No way can you hide it in the hold of a commercial aircraft. No way can you transport it in a truck.
I don't know whether or not you could successfully put it in the hold of a ship below the waterline and covered with shielding and successfully get it into a port or not. Supposedly the nuclear material that was being smuggled to Israel for their nuclear weapons program was detected on a ship in the Med back when Nixon was President, and that was the reason (again, supposedly) that he put US forces on alert worldwide and caused some excitement. Some of the older members of this forum may remember that. (That Nixon did that, not the part about the detectors, the ship in the Med, the fissile materials, etc. - noone has ever admitted to that.) Of course...I could be completely wrong here. No such detectors REALLY exist, of course.

I do not believe you are correct.

I do not believe we can detect a nuke from any significant distance when reasonably shielded.

For example if one is placed at the bottom of a filled oil tanker I seriously doubt we would have much luck at all detecting it.

That is prior to detonation…