The bomb we dropped on Hiroshima, Little Boy, has a blast yield of 16 kilotons. It created a mushroom cloud several miles high. It completely destroyed everything within 1 mile of the epicenter. The blast was so bright that it burned people's shadows onto the pavement. Everything out to 1.25 miles was seriously damaged- structural failure of buildings and bridges, etc. Everything out to 3.5 miles suffered some damage- broken windows, overturned vehicles, etc. Fires were ignited as far as 4.4 miles away. Between 70,000 - 100,000 people died in the blast or within hours of it. Another 75,000 were seriously, permanenty injured. The birth defect rate in Hiroshima even to this day is 100 times higher than in the US. And that bomb was only 16 kilotons. The Castle Bravo blast that we detonated as a test at Bikini Atoll in 1954 was 15 MEGAtons. That's almost 1000 times as powerful as Little Boy. It was so powerful that it formed a crater on the ocean floor of the shore of Bikini Atoll.
The average payload of an ICBM is 5 megatons. These have a direct blast radius of 1 to 3 miles with a concussive blast out too about triple that distance. This would create a cloud of radioactive fallout about 10 to 20 miles in diameter that would then be carried by the wind. The radioactive contaminants would be washed to ground level with the next rainstorm. It would remain in soil and ground water for years or decades depending on concentration levels.
Well your average normal nuclear bomb spread depends on the tonnage of the warhead, wind speed, direction, & density altitude. The moisture content or humidity also plays a small role ( I think that it's negligible) The first 2 dropped on japan were a surprise for all involved, although it spread for miles from the epicenter the damage dropped off dramatically. We now know that just because there was no visible damage 50 miles away, there was enough radiation to inflict great harm or even death. When Chernobyl melted down, it wasn't a bomb but the danger is the same radiation was picked up in France & Spain-thousands of miles away. Today we actually have back pack nukes, that are carried by soldiers & will do a great deal of damage for a mile out to 3 miles. The average today can destroy 50 miles or so