I visited the place in 2006. With a DRSB-01 Geiger counter, modified to output the data to a GPS-equipped datalogger. The radiation level in the Chernobyl village itself was roughly the same as in Kiev. It got a bit worse in The Zone, a bit more worse in the inner zone, and the Geiger sang a merry song in the very vicinity of the Sarcophagus. But even then the radiation level was fairly low. (Sorry, I don't have other numbers than count-per-minute records from the Geiger; it was not calibrated.)
The short-halflife isotopes are decayed by now, the long-halflife ones aren't active enough to pose much risk. The principial radioisotopes in the area are Sr-90 and Cs-137, the latter comprising the majority. While Sr-90 accumulates in bones and presents some long-term hazard, caesium behaves like potassium, accumulates in muscles, and its biological half-time counts in weeks; you will literally piss it out in few months. And you won't get much into you anyway, as it is by now virtually all bound to soil particles or to solids in the biosphere; assuming you won't lick your boots, eat the dirt, or ingest the local mushrooms.
We even got to see the Red Forest. The roads themselves are pretty much decontaminated; but even off-road the radiation levels aren't catastrophical. A day won't hurt you.
I wore a thermoluminescence dosimeter, just for sure. After a day in The Zone, the total dose I got was still below the limit of the device's resolution.
It's a nice place to visit. And it's peaceful, as all the cowards, anonymous or not, go somewhere else instead.