Kathy - as I've said above, I don't think there is any difference in beginning in Tokyo vs Nagano, all things being equal. Of course, you might consider jet lag and an acclimatization period which would argue to begin in Tokyo. Relax, recover, get your feet on the ground.
If you don't like that thought, I can give you details on how I've arranged schedules when I've had routes where there were multiple possible directions. I lay everything out on a spread sheet with dates, then check my preferred hotel accommodations for each city. ( I learned this trick after booking multiple places in various Spanish cities, then discovering that Barcelona had a major convention with very high prices and low availability for the hotel dates I needed. I had to redo all the bookings....) If hotel accommodations look fine, I lay out the activities, performances, exhibits I am interested in in each city. Not infrequently, there is a problem with something not being open on a day I've scheduled a city. Then I have to juggle.
Re the Hakone visit - I have always done overnights, but my trips didn't include the same itinerary and number of stops in one go as yours. (I've had recent trips which have included your stops, but not all on a single visit to Japan. Multiple visits since re-opening in 2022.) Ordinarily, I would suggest placing Hakone in between Kyoto and Tokyo - as a stop on the return to Haneda. However, with your itinerary which includes flying from Hiroshima (or Osaka????) back to Haneda, this isn't a good solution. It seems that your options might be connecting between Hakone and Nagano (or Takayama or Kanazawa) by train or traveling Tokyo to Hakone for an overnight then back to Tokyo for departure to Nagano - awkward. If you reversed your trip and headed from Tokyo toward Kyoto and on to Hiroshima first, then an interim stop at Hakone would work well for an overnight. Continue the loop from Kyoto to Kanazawa/Takayama/Nagano (if you've figured that transport out.) A car would simplify the process.
Hakone is both loved and hated. I am a hiker, art lover, history lover, outdoor explorer. The area holds much more of interest for me that I could include in 3 days much less one - I've visited multiple times. Others are much less interested and want to experience the circuit of train, cable car, ropeway, cruise ship, bus. If that is your interest, it can be accomplished as a day trip from Tokyo (simplifying scheduling). Start early and be prepared for crowds and delay. I have always used taxis at some point in my trips as the transport is not quite as efficient as indicated in the advertising literature and travel brochures.
Best of luck.