I looked into this last year and may do it sometime in the near future. You can't just go around Chernobyl and Pripyat willy nilly by yourself. You have to get clearance to access the exclusion zone but this isn't too much of a problem as there are companies which run tours.
From the phonecalls I made, the day tours consisted of departing Kiev in early morning for the checkpoint on the border of the exclusion zone. Here you are kitted out with the stuff you need, food and water from outside the zone, given the instructions you need and then you all pile onto a bus for the tour. Some of the tours even involved a trip to the power plant but for obvious reasons, such a visit would need to be very quick.
I was quoted a price of $200USD for the entire day trip including all equipment, security processing fees and food/drink.
The main reason I didn't go was because the company I enquired with didn't allow photography and I wanted to go purely for photography.
For good pictures, there's a photo book by Robert Polidori called "Pripyat and Chernobyl" although the only copy I could find was in German and is called "Pripjat Und Tschernobyl".
