I've been there in 2008. My advice:
Stay on the ROAD. The soil can still contain high levels of radiation. Roads are better.
Don't stir up ****.
Get a guide. Really, get a guide. Pay for a GOOD guide. Not because of safety (well also a bit), but they know all the really cool hidden ****.
Don't worry about radiation, we were nearly a stonethrow away of the sarcophagus and I had a healthy kid earlier this year. No additional tentacles besides the one obvious.
Excellent advice and I'd strongly recommend that you take it. I know the former communist world quite well, and a good guide is probably the best investment you can make while there. Staying on the road makes total sense - asphalt is a lot safer than the countryside.
True. It is no longer a monolith, but has become a number of independent states of which (excluding Russia) Ukarine is by far the most important. Also worth noting is the fact that, because of the direction of the wind on that fateful day in April 1986, most of the radioactive material blew over, onto, and into Belarus, rather than Ukraine itself, so while the reactor is in Ukraine, most of the radioactive damage has taken place in Belarus.
Actually, I have visited Belarus on a number of occasions, while observing elections, including, most recently, the appalling case of flagrant fraud which occurred there last December, when the incumbent President Lukashenko was declared the victor in an election best described as an outrage to civilised behaviour and a flagrant abuse of human and civil rights.
This was my third visit to the country. The first occurred in October 2004 (observing an election) when I was sent to the Gomel region, close to the border with Ukraine, (and, as the proverbial crow flies, very close to Chernobyl), which is, as it happens, one of the most radioactive places on the face of the planet. While poverty and some degree of squalor were evident, I can honestly say that I have never seen such a defeated and depressed air about the people, I would term it as bordering on despair. In fairness, we were given the option to visit (or not as preferred) the contaminated regions, villages and polling stations. I chose to go, partly to bear witness to what I saw and to observe a flawed ballot in a region where I was fairly certain the authorities were convinced we would choose not to visit.
In Belarus, to this day, the authorities do not label the dairy, or place of origin, of much of their dairy produce. So no-one knows where it comes from, or, whether it comes from a contaminated region. The birth rate of the country has plummeted (while the President had expressed a desire for a marked increase in population, to the silent horror of his people. Belarus, he said, should be able to provide for 30 million people, not the paltry 10 million currently living there). We know about the effects of the nuclear accident on large numbers of the children from the affected regions, and I myself have known people who have played host to Chernobyl children when they visited the west. According to official sources and statistics, radiation is no longer a problem in the soil of the country. I think we can treat these sources with a degree of scepticism. I mention all of this to tell the OP that there are consequences to the disaster that happened in April 1986, consequences which are still felt in that part of the world.
Therefore, to a certain extent, while I understand the OP's motivation - and would probably travel there myself if opportunity offered, nevertheless, a thirst for adventure does not mean that one should neglect to take prudent precautions. And treat the place with respect. This is a graveyard. And worse, this was one of our world's most grotesque tragedies.
Good luck and enjoy yourself.