The OP limits the question to “contaminated areas” - the first that came to my mind is Bikini Atoll in the Pacific - site of extensive nuclear testing. I agree that the amount of space on earth rendered “no-go” by pollution is minute. Most places like bomb ranges are far out of the way and of little value to humanity anyway, so we wont be getting hemmed-in anytime soon.
However, if you expand the question to just no-go for the average person, the list gets interesting as to the reasons why:
Area 51
North Korea
The city of Mecca, Saudi Arabia (depending on your religious persuasion)
Well, most of the US is no-go for most people; it’s just not quite the same set of no-go areas for any two people. There are a great many places I can’t go because I would be trespassing, but for every one of those places, there are a few people who go there without trespassing.
Times Beach, Missouri was more or less a no-go zone for a while due to dioxin contamination as a result of some knucklehead who mixed industrial waste (from a plant manufacturing Agent Orange) with used crankcase oil and sprayed it on city dirt roads as a dust suppressing measure.
Apparently the town is no more, and the first several inches of soil have been stripped and incinerated. There’s a Route 66 highway park on the site now, and there’s apparently no significant dioxin contamination any longer.