Hakone is very much on the tourist path, it's one of the most popular destinations for people from Tokyo... if you want to go off the beaten path, go mountains, onsens in Nagano or even Yamagata etc...
I went to tsukiji fish market last August, you have to go there early morning. Long queues. Etc, lots of people with cameras and lots of people don't want to get photographed.
It's also very very low light, since it's early morning, etc... pretty much digital camera heaven. I didn't get a single decent photo there, but it could just be me. I don't like waiting in queues and I like to walk around and find things, or seat down and eat. The food is great at the market. So enjoy!
Here's few photos from Japan, most of them off the beaten path. (I think)
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I want to visit Hiroshima, my ex went there and she enjoyed it a lot. You didn't say how long you would be there or exact dates. But personally in October I would head to North Japan, even as far as Hokkaido (awesome seafood there) and chase their Autumn.
http://www.japan-guide.com/e/e2014_where.html
This map should give you rough indication of where to go depending on the dates you are there.
http://www.japan-guide.com/e/e2014_when.html