Dear Kareline,
It's a very inviting itinerary - visiting Japan in April is one of the best times of the year for sightseeing. What may prove to be a little difficult is going from the Kurobe Alpine route directly to either Fuji or Hakone, this because the Japanese Alps are right in the way. I would suggest traveling to Hakone first as it would be making the best use of the JR Pass (if you have one) and make a day trip / one nights stay from Tokyo later on. This would make the most sense budget wise.
I made a small list of ticket prices below to see if a JR Pass would be of help.
(usage period 17th of April - 23rd of April)
Tokyo - Hakuba ¥ 7,870
Hakuba - Toyama ¥ 3,670
Toyama - Hakone (Odawara station) ¥ 14,340
Odawara - Tokyo ¥ 3,440
For a total of ¥ 29,320 the 7 day JR Pass is 28,300. A JR Pass could thus be an option and help you make slight savings. You can also use the JR Pass in Tokyo and from Toyama to get closer to the Alpine route, adding a little more to your savings.
Note: that I assumed that you are traveling from Toyama to Hakone, this would be different if you complete the full Alpine route and travel from Shinano-Omachi. This would take about the same amount of travel time but the fare would be slightly lower depending on what trains you travel on.
Lastly, no mater how you travel the trip from the Kurobe Alpine route to Hakone will take about 4-5hours by rail, so be sure to bring a good book to read or some good company to keep you occupied :)
I hope this helps!
Daniel