Touring Chernobyl feels distinctly odd. The name conjures images of a doom-ridden wasteland, but the reality is very different. Even deep inside the exclusion zone there is generally only low radioactivity, roughly the same as normal background, and it has turned into a pleasant green wilderness, marred only by a scattering of decayed buildings. We could wander around fairly freely with only very minimal precautions. The main problem (beyond the reputation) is there are still radioactive particles in the soil, etc, so it is unwise to go digging around and it is certainly not a wise place for long term residence.
We visited various eerie abandoned buildings, especially in the abandoned Soviet city of Pripyat. We wandered through an abandoned school, a grand sports center, a never-opened funfair. All slowly decaying and returning to nature. The road into Pripyat has been mostly taken over by trees, with a relatively narrow track kept open.
The high point of the tour was a stop near (but not too near) the notorious Reactor 4, where we had a good view of the reactor building now shrouded in the old sarcophagus. The immediate reactor area is still dangerously hot, so for safety the new protective sarcophagus is being built a short distance away, in two halves, and will then be rolled into position over the old sarcophagus for better containment.
I visited on a day tour run by SoloEast (aka TourKiev) from Kiev. It worked well and I recommend them.