It's hard to classify an area as simply "Radioactive" or "not Radioactive" because we're all exposed to varying levels of radioactivity all the time.
The problem with Chernobyl is, like all fission reactors the spent fuel that wat scattered around the area is a nasty cocktail of all sorts of radioactive sources, some with half-lifes of a few days and some with half lives of thousands of years.
The risk for short visits is relatively slight providing that you don't risk ingesting any material.
Some radioactive sources emit what are called alpha particles, they have a short range and your skin can stop them but if they get into your body they can do a lot of damage
Polonium 210 is an alpha emitter - enough said?
Here's an interesting article on a visit to the exclusion zone
http://www.spiegel.de/international/0,1518,411 285,00.html