3 weeks summer trip to japan

This is the planned trip:
1st week at Tokyo - mandatory.
2nd week: 5.5 days trip - from Sunday morning (13/8) to Friday afternoon(18/8). This trip must and at Tokyo.Suggested itinerary: Tokyo-hako0ne-atami-shizuoka-kyoto-osaka-tokyo
3rd week: 4 days trip starting 20/8 morning- to 24/8 morning at NRT. Suggested itinerary: Tokyo-nikko-sukatsu-shiga kogen-omachi-japanese alps-matsumoto-tokyo-nrt
My main question is about renting a car versus using train services. I have found that 24 days JR PASS for 2 people will cost 804$. I will have to add the cost of sending our luggage from hotel to hotel (2 suitcases) and that will cost abouut 600$. Rebtig a car 11 days (13-24/8/17) will cos about 750$ + fuel (250$)= 1000$. This is much cheaper and off course much more flexible.
Please recommend. (car or train. are suggested itineraries dood choice?)

If the car travel will be cheaper, it's your decision. JR Pass is until 21 days only that costs USD 510 for ordinary.

Honestly, you do not have to go back to Tokyo just to travel in each leg. Travel sequentially without going back to Tokyo.

What places did you include outside Tokyo when in the city that will let you use JR Pass? Although probable but I think 21-day JR Pass will be too much.

Further, there are buses involved in your travel that is not part of JR Pass, especially if you are to take the Alpine Route.

i dont get why you cant travel with your suitcases in the train? You could avoid the additional 600...

also keep in mind that if you go for the car approach that many road in japan are toll roads (especially in the japanese alps) - and they are NOT cheap. and you dont want to drive those small toll free roads there (it will take you many hours more). so this will add also quite high amounts to the car option.

Indeed there is no reason for baggage service for such short distance. I am only seeing a baggage service for Alpine Route no more, no less.

To OP, if you really plan to rent a car, also consider the car transfer service in Alpine Route which will cost you around USD 250 on top of your car rental fees.

Even the Alpine route, you will not need to forward your luggage. If you get the pass that goes from Nagano to Toyama, it is very simple to travel back to Nagano. It's less than an hour away by shinkansen.

It is possible that you only need a 7 day JR pass, and some other passes, such as the Harkone free pass. On other days, an IC card or a local pass will help, such as a one day bus pass in Kyoto. The other thing you may need is a single one way discount ticket from Tokyo to Osaka or Kyoto.

All this would be far less than renting a car.