Must-see historical sites?

Hello, I'm planning to travel to Japan for the first time in April for 14 days, planning to stay in Tokyo and Osaka, exploring them and traveling out from those 2 areas (I understand that Osaka is the better place to stay for traveling compared to Kyoto). I love anything historical and have seen from research that there's many great museums, castles and historical towns (especially samurai ones), although this has overwhelmed me a bit as there's so much. So what would you say are the unmissable historical areas and museums I should prioritise? Can be any period up to WW2 and really 3 hours travel max from either Tokyo or Osaka.

I've already heard of several good museums in Tokyo and places to go to such as Kanazawa, Nagoya (museums mainly), Hiroshima, Okunoshima, Matsumato castle, Sekigahara, Nara park, Kakunodate, or the Gifu region (Magome, Hida Takayama), which have all stood out to me so far. Although of course I'm not sure how good they actually are in person and as you can see that's already a lot for 14 days which I may not be able to cover – I understand people commonly fall into the trap of having too much planned.

I'm also aware that April will be a relatively busy time, in which case are there any underrated historical areas that you recommend? I understand that Kanazawa is a less-visited area for instance.

On another note, if anyone knows any fun gaming places to go to, which I imagine are mostly within Tokyo, that would also be very appreciated as I’m an avid gamer too who knows very little about what the arcades are like there.