If you can't find internships on the site I would suggest searching the company sites. I have seen many utility postings for interns. I'm sure some of the other Nuclear associated companies would have openings for your interest.
You can follow either of the two links below to find out who owns the licence, or is responsible for the plant operations. For the second link you can click on the state, then find the appropriate plant in the sidebar.
http://www.nrc.gov/info-finder/reactor/#AlphabeticalListhttp://www.eia.doe.gov/cneaf/nuclear/page/at_a_glance/reactors/states.htmlHere is a list of all companies that have postings on nukeworker. If you go to their site, they could have internships posted there.
http://www.nukeworker.com/job/list_companies.phpSince I haven't been in search of internships I can't help a whole lot, but they are out there. These are a few good places to look.