14 day itinerary

We're 2 couples in our sixties. We plan to visit Japan, for the first time, on October 2019.
I would like to hear your comments on the itinerary I've planned:
We land in Osaka on the 7/10 at 20:30. We'll head to a hotel on Namba area.
On the 8/10 we'll head to Hiroshima and the island of Miyajima.
On the 9/10 we move to Kyoto where we'll stay for 4 nights, (including a day trip to Nara).
On the 13/10 we plan to hire a car and drive to Takayama.
The 14/10 we'll drive to Matsumoto through the Kamikochi valley.
The 15/10-16/10 we'll spend in Hakone.
On the 17/10 we go to Tokyo where we return the car and stay for 4 nights.
Our last night the 22/10 we'll lodge in Narita since our flight back leaves on the morning of the 22/10.
Thank you.

I would recommend two days in Hiroshima, and visit the city and Miyajima on separate days. Visiting them on the same day can be rushed.

There is no need to rent a car to visit Takayama, Kamikochi and Matsumoto. Indeed, if you wish to enter Kamikochi, you cannot bring a private car (only public buses and taxis permitted). Instead, take public transport from Kyoto to Takayama, Takayama to Kamikochi, and then Kamikochi to Matsumoto. Driving in Japan can incur expensive tolls, parking can be hard to find and expensive, and driving through city streets difficult.

...not to mention that renting a car in Takayama and leaving it in Tokyo could incur some expensive drop-off charges.
Getting from around Namba to Hiroshima will take you 1¾-2 hours. I concur that adding at least half a day to see the city and Miyajima is worth it. For Miyajima, the shrine does not take that long, but Daishoin could take you an hour to 90 minutes, yet is so worthwhile. You could skip Mt Misen if you don't want the climb.
https://goo.gl/g8HWjh
Hiroshima City has some gems as well - far beyond the Peace Park. Please don't be another person who just sees the park and leaves the city. The Shukkeien Garden is wonderful, plus the Mitakidera Temple and Okonomi-Mura are well worth your attention.
https://goo.gl/fAz4ax
Himeji is also between Hiroshima and Kyoto, with Japan's finest original castle, Kokoen Garden and Mt Shosha.
https://goo.gl/65ZtRi

Two nights Hiroshima, three nights Kyoto.
Don't drive - you might not know how slow it actually is - wastes a lot of time, even up to the mountains of Takayama and through to Matsumoto.
You could change Hakone as well - it is over-rated compared to a lot of other places in Japan(just that many people never get to see those). You could continue from Matsumoto to Nagano and even Nikko before returning to Tokyo.

Thank you for your answer. If we do stay in Hiroshima for 2 days l have to take off s day somewhere else. We do have only 14 days. Where would you recommend to deduct a night?

I would indeed add one more night to Hiroshima.

Where to take out a day depends on your preferences. I really like Kyoto because there are many historic sights to see so I would not trim a day. Tokyo is great as well as it is in complete contrast.

I would probably skip Hakone as a separate stop, unless visiting an onsen is high on your list. The round trip was nice, but other locations (Nikko, Kamakura) that could be done as side trips from Tokyo I liked better.
Or visit Nara from Kyoto.

Depending on where you fly in from. You still may be jetlagged. So attempting a rush day of Hiroshima and Miyajima isnt advisable.

I also agree with the others about you transports options and places to visit. What you have done seems difficult and costly.

If you skip Hakone and assuming you wanted to go to Hakone for the onsen in the first place you have 2 nights at your disposition. You can use one for Hiroshima and one for onsen experience in Hirayu onsen / Okuhida or some along your travel.

As others said a car wonft be useful for going from these kind of major destinations you have listed. However if you plan to visit other smaller spots on the way (eg Ainokura instead of Shirakawa) itfs a different story. (But it doesnft seem you have time for a lot of side trips. Being in 4 it might also mean that it is cheaper than train (youfd need to do the maths). You could also consider to rent a car just for a day if you want to go somewhere rural. Driving in Japan itself is easy, relatively slow (for planning purposes just take google maps times) but there are extra costs for express ways (there might be some passes similar to JR pass, have a look) and parking. But if you are willing to pay for parking, itfs not overly complicated to find a parking lot. However in many cities there are simply no free parking options anywhere. Really only in quite rural areas is parking free. You should then also consider your car as a g5th guesth when making your hotel reservation to get a parking lot.

Enjoy your trip to Japan!