How about telling us a little about what you're interested in, so the answers can be more useful? Are you more into big cities or more into nature? More into anime culture or more into traditions and crafts? More into sports or more into seeing museums? – to give some examples.
It sort of depends but there are 2 historical atomic bombing sights in Japan that are worth seeing. One in Hiroshima and another in Nagasaki. I have been to the Nagasaki one and there are heaps of beautiful peace statues and a historical museum describing the events and there are some exhibits that they let you touch that were in the event that got exposed. I don't know much about the Hiroshima one but it's just a recommendation.
Otherwise, there are websites that can recommend great tourist spots in Japan and I believe Google maps has a feature called hidden gems that recommend beautiful places few people know of. I have used that before to find amazing restaurants and Zen gardens in Japan that is just wonderful and normally a must see.
Otherwise no matter where you go, the Hot Springs or onsen are a must try being one of my faverote things to do in Japan that I have to do everything I go (including drinking qoo apple juice with the best apple taste but that is just me)
