I didn’t know this, but there’s apparently a company that sets up tours to Chernobyl and allow you to roam the nearby abandoned town of Prypiat with a tour guide. The tour guide carries around a radiation detector and shows you the amounts of radiation still in the area (not deadly amounts, but definitely nothing you want to stay in for a long time).
Here’s one man’s photos from the tour sometime last year. According to him, the tour was easy to book and very accommodating to his travel needs. This actually sounds like something I’d like to do.