Another option is that many plants offer some sort of tour to local groups (boy scouts, schools, etc.). While the tour doesn't usually go inside the plant, you can see things like the control room simulator, etc. Ask the plant's public information people about the tours. Some more specialized groups actually get tours inside the plant (but outside the actual vital areas). The groups include ones like the local American Nuclear Society section, local government, the media, etc.
The idea about trying to get in as a temporary worker is a good idea. Most plants have arrangements with staffing companies - call the HR department and ask who supplies their supplemental workers.