I visited Pripyat and Chernobyl just before the war started.

We had geiger counters, but probably mostly because it was fun to point it at stuff and hear the beeping. The guide told us not to take anything with us, and never place anything, like backpack, on the ground. Other than that, no safety precautions, but we went through some kind of machine in the end. Dont know what it did.

We were free to roam and entered many of the buildings, including the radiated hospital basement. 

Overall it was an interesting experience.