Your navy nuclear experience will be a plus for you regardless of rate if you want to work at a civilian plant when you get out. After 6 years of the nuclear navy, you very well may want to look to a different field

But in all seriousness, do your job, do it well, stay out of trouble, and learn as much as you can. Before your EAOS, if you are still interested in the nuclear field, I'd start doing research on specific sites, and making contacts with people that work at those sites. I expect nuclear power to grow over the next 10 years at least, so there should be an opening to your liking. The hiring process can be a little stressful, but your experience should help you crush the tests and interviews.
Good luck with the Navy! I did my 6 and, in the end, it was a pain in the ass, but well worth it.