Itinerary for Japan

Self-touring in Japan is not difficult, I think you will be pleased with a DIY itinerary that you can control to your liking. I would suggest studying some maps of the larger train stations before leaving. For instance, several Tokyo stations can be confusing, but there are many English speakers available to help and English signs. A little knowledge of the stations can be a time saver.

Have you checked your itinerary against one of the travel apps to see the journey times and departure/arrival options?
https://world.jorudan.co.jp/mln/en/?sub_lang=nosub
https://japantravel.navitime.com/en/

From my perspective, you've included lots of great highlights, but the actual time at many of the locations would be too brief for me. 2 nights = 1 full day - for instance 2 nights in Kanazawa only allows for a one day trip to Shirakawa, not also time to explore Kanazawa (unless you can time your trains well allowing for partial days on arrival and departure - that may be possible). I do tend to be a "slow" traveler, so my preferences are not everyone's.

Run your itinerary against the cost of a train pass. The prices went up significantly a few years ago and it may not pay back. https://www.japan-guide.com/railpass/ Also, the pass might not be good on routes to Nikko depending on which train company you use.

I think your order makes sense. I don't know that clockwise or counter-clock is preferable.

I can recommend this company for a Shirakawa-go day tour from Kanazawa. I used them 9 months ago. I booked directly on this website. We did the Shirakawa-go and Gokayama World Heritage Village Tour - English spoken, very organized, very efficient and well managed. https://whitering.co.jp/index.html

Which airport do you arrive in? I'm assuming Haneda or Narita. Check the transport to Nikko from the airport. It may be preferable to visit Nikko as a day trip from Tokyo.

Edit - Yes, it can be very overwhelming to plan!!!! I have found the on-the-ground to be easier than the decision-making!

We did 8 days prior to a cruise from Tokyo to Hong Kong, stopping in 5 Japanese ports in 2015 and di most of the places you mentioned in your proposed itinerary.

We took a local Japanese company's tours going to Nikko (lived that one) as well as Kamakura and sites in Tokyo. Also, we took a multiday tour of Kyoto and Nara that included the high speed train (forgot the name). We did an afternoon in Nara and three days in Kyoto. Our Kyoto tour included two days of sites in that city with another day on our own. We loved Kyoto. Recommend taking tours, since the sites are not real close to each other, except the Philosopher's Walk, which we did on our free day, having to take a taxi each way, which cost a bit.

We did Himeji Castle, Osaka Castle and Nagasaki on the cruise as well as a few other sites.

First, I would go north to Nikko on a day trip, do Tokyo and other day trips before moving south.

Since you have traveled extensively in Europe there should be no problems in Japan. Same type of stuff. If you do similar itineraries in Europe then same in Japan.
Travel experience style is personal. One night, two nights, enroute stops, packed days, etc. It is all your style.
I am headed for Taiwan shortly for a month and my style has been hardened over the years and I figure it all out based on that. I do not post itineraries for review as the replies would only cause endless more research of which I have already done. You cannot see and do everything.
Travel is always a compromise. Do your thing.

I would sugges Miyajima as a day trip from Hiroshima. Very easily done.

The other thing that is very important, if this is your first trip to Japan, is to learn the unwritten etiquette rules:

Japan--Tips and Customs for a Successful Stay

You may also want to read up on the Konbibi--Japanese convenience stores. They are everywhere and nothing like the ones we have in the US. (Even if the names sound familiar).

Another big thing to realize--there is no tipping. None. Zero. Nada. It may be considered an insult. Don't do it.

We are planning a similar trip in late October, though we're doing it in a slightly reversed fashion and we're staying for 28 days, so adding in few more places where we'll stay for a few nights (Matsumoto, Kanazawa, Okayama/Kurashiki and are extending our stay in Tokyo to 5 nights and Kyoto to 7 nights (will do a couple of day trips from there).
We're flying into Tokyo (Haneda) and home from Osaka (KIX), so we'll end our trip with the stay in Kyoto and the last night will be at an airport hotel at KIX. So the route will be: Tokyo-Matsumoto-Yamanouchi-Takayama-Kanazawa-Hiroshima-Miyajima-Kurashiki-Kyoto. Plans right now are to rent a car when we leave Matsumoto and return it when we get to Kanazawa.
Happy planning!!

Hi, does anyone have any recommendations on whether my family should spend the last 2 nights of our 2 week Japan trip at Lake Yamanaka or Izu? We will not have a car and plan on taking the train to Narita on our last day.

What is the transport from Lake Yamanakako? Bus and train?? Not clear to me if you were hoping to get to Narita on the same day as leaving from Fuji Five Lake area, but I wouldn't risk catching a plane when leaving from the region. I confess to being conservative on departure day travels - you may feel differently!

Izu - not sure where you mean. Somewhere on the Peninsula? Check the train schedules from the location you are considering. https://world.jorudan.co.jp/mln/en/?sub_lang=nosub
(My personal preference (I fly in and out of Narita) is to stay in Tokyo or at Narita the night before a flight. A number of hotels near Narita and Narita city is itself a charming spot. Again, personal choice. )

I strongly suggest you do not travel until late Oct, at the earliest. Foliage season in Japan is awesome and you don't want to get there before the leaves turn color. Also, do note that the season starts on different dates according to altitude and latitude. For example, Nikko and Takayama/Nagano will have foliage earlier than the other cities.