I did find a visitor's center but no info on whether the plant itself can be visited.
Not really. It's still a functioning power plant, and as such there are safety concerns with letting people explore a place.
There is a Three Miles Island Visitors Center, which has exhibits and video displays.
The company which operates the plant, Exelon, has their Three Miles page online as well.
A journalist for Bloomberg was taken on a tour, however, that may have been a press tour only. You could try contacting the visitors center and/or Exelon and see if there's a press tour or similar which you may be able to join.