We've driven around Bremerton and found that there is one hill in a residential neighborhood (military families mostly I think) you can drive up. At the top, there's a ton of blackberry bushes and a great view of the carriers. Last summer we made the effort to find that spot because there were five carriers there!! Quite a sight! It took a lot of looking, because so much of that area was fenced in, but it was worth it.
I want to say that we were roughly here: to: 47.553502,-122.661585 - Google Maps
-- but I can't be sure, it was more than a year ago and I wasn't driving. It could also have been on McCall or Summit. But we did have a great view of all the carriers in port. I don't know if the military freaks out about it or not, but if you had a set of binoculars you would be able to REALLY see them better.