Like other said, leave out Nagoya.
Miyajima is not a tourist trap - it's truly amazing and worth going if you are in Hiroshima - 10 min ride away on the ferry (which is free with a JR pass). I suggest you hike there by foot a little too.
I have a post on Miyajima on my blog, as well as other useful Japan travel tips which you can check out -
Smart & Cheap Japan Travel. The book that I am publishing soon shows how to travel the right way in Japan and do so economically.