If you are going early may, check out Tateyama Kurobe Alphine route.
Its an amazing place. starting with walking thru a giant dam. then taking a slanted cable way, shuttle bus, ropeway... at the top of the mountain, can see the town of Toyama. You'll see snow walls of 20m high. I like that although its a man made attraction, it is not typical and touristy. and it is very educational. Going beyond the route, you can visit unazaki onsen, whose river is connected all the way to the dam. They even have a workers train that brings you in to the mountain areas where the workers of the Japan electric works at to harness hydro power.
Its quite far. But you can take the Hokuriku Shinkansen there in about 2.5 hours. I would think its quite worth going. I got the chance to see awesome sunrise and stars at 3000m height.
Alternatively, can visit Nikko. Nikko is also about 2 hours express train away from tokyo. UNESCO World Heritage Site. Chuzenji Lake and the Waterfall is awesome. Very striking.
Another place is Hakone. Which is readily accessible in 1 hr. The Onsen is good and there are many museums around worth going. Like the Hakone Open-Air Museum, Pola Art Museum, etc. The Pirate ship was quite fun too. Not the mention the jigoku ropeway.
Then also, you can visit Mt Fuji (Not the fifth station) for the shibazakura
This is at the 5th lake i think. First lake is kawaguchiko which is very touristy. Enroute can visit the caves somewhere near 4th lake i think. Get a ryokan that enables you to admire Mt Fuji frm far.