Travel advise around spring

Hello. I was hoping to get some information around traveling to Japan. Its not gonna be this year but I would love to go to Japan for my birthday at some point (3rd of May which I believe is Constitution memorial day in Japan, during golden week). However I would love to be able to see the cherry blossom trees. Sadly I read here in some post when I googled that golden week is too late to be able to see them. Would it be better to not go during golden week as its likely to be more busy as its a national holiday and go earlier in the year?

The plan would be like a week or two at most as I would love to travel around a bit. Not really sure what I would be doing outside of visiting different cities. Maybe also seeing some nature (I don't know how feasible it is to go to Mount Fuji or at least some hotspot close to it for some photos). I really love to travel to see nature and historical stuff so I want to try and get some of that stuff checked off.