16 days Japan

Please help!! I am planning 16 days trip to Japan this September. We will be flying in and out of Narita. My plan so far is listed below:
Tokyo 10th to 14th -sightseeing in Tokyo
Kyoto 14th to 18th Sightseeing in Kyoto with a side trip to Nara or Kobe
Hiroshima 18th spend the day and stay the night in Miyajima Island
Osaka 19th 21st Sightseeing and day trips
Hakone 21-23
Tokyo 23-24
We are planning on purchasing the 14 day JR pass
Is there any other destinations to add to this, or should I reduce the time on the above destinations, any comments will be appreciated?
Also, want to know if its worth to make a trip to Fuji 5 lakes area and doing a trip to the mountain?

Pretty standard itinerary. Not too fast nor too slow. You could consider the following:
- stay only in Kyoto in Kansai (ie add the Osaka days yo your Kyoto stay, removing one hotel change and adding flexibility to your daytrips)
- be aware that the Torii on Miyajima is under renovation. @rkold (other regular poster here) found out that itfs currently not totally covered though.
- I am not good at JR pass calculation so just make sure it pays off. Within Tokyo and Kyoto it is of minimal use. So if it pays of for the long distance trips then fine. If it is just about to pay off then youfll need to decide based on pros&cons
- Regarding Fujigoko, what do you want to do with gthe mountain g? See it? Climb it? Climbing will be too late in September. Seeing canft be guaranteed from anywhere but obviously Fujigoko is the closest place. But if you are lucky you can see Fuji easily from Tokyo.

Enjoy your trip to Japan!

Your itinerary looks good.

I think this is a good calculator for the JR pass: https://www.japan-guide.com/railpass/

It can work very well if you are able to use it to and from Narita-depending on how your 14 days pan out and what time you land on arrival.

It could also be very hot and even typhoon weather in September so be aware you might want to have some 'indoor' plans up your sleeves.

Have a wonderful time in Japan.

Thank you both for your recommendations.
I will have to do some calculations to find if the JR pass is worth the cost. I am landing around 6.30 pm and will not be using it to get to Tokyo on the 1st day, if I activate it on our 3rd day we will be able to use it to get back to the airport.
Like I said need to look into it.
So just spending the one night in Hiroshima or Miyajima make sense. Our plan was to climb Mt Fuji? What I was reading indicated that the climbing season is ending in mid-September?
I hope at least to see the mountain from Hakone and spend the day there.
All my activities so far have been based on outdoor attractions! Can you suggest any activities for rainy days? Planning to visit Team lab borderless in Tokyo which is my only indoor activity.

Last day for Fuji climbing is 10/Sep:

http://www.fujisan-climb.jp/en/season/index.html

IF weather collaborates.

Regarding indoor attractions, have a look at the webpages of each of your destination to have some backup in place. With typhoons the good thing is that they are over in a day (or less) and weather beige and afterwards tends to be nice. But if you are in a place hit by typhoon you donft want to be out there in the rain.

I am not sure whether JRP14days will pay off for you because round trip ticket Tokyo|Kyoto|Osaka|Hiroshima\Tokyo costs around 40000 yen.
If you come back to Hakone on September 20, JRP7days starting Sep14 will pay off. In and around Tokyo, using Suica IC card is enough and most convenient.

Mt. Fuji can be seen from Hakone, depending on the weather condition.

I agree with staying in Kyoto longer and eliminating Osaka. You can do all the side trips you were going to do from either Kyoto or Osaka and you will save a lot of time. By the way, I would choose Nara over Kobe.

I'm butting in here. Champ had mentioned going to the five lakes region, but replies indicate going to Hakone, seemingly in place of the five lakes area. I'm dealing with a similar debate: if I have to choose one, and the goal is good viewing of Fuji, should I pick Hakone or five lakes?

My idea was to stay at Lake Kawaguchi and spend the day climbing the mountain. only arriving on the 10th Sep, too late to set foot on the mountain. We have decided to keep an eye on the weather report and take a day trip to Hakone during our stay in Tokyo. I already have 5 days in Kyoto do you think we should visit Nagoya instead of Osaka?

Instead of Osaka you could do one night at Hikone, see a little of Lake Biwa and go to beautiful Hikone Castle. There are some nice hot spring hotels there I think.

I very much enjoyed Mt Hiei, which is the other side of Biwako from Hikone, home to Enryakuji, a temple district (World Heritage listed). The main temple is closed off for renovations but there is a lot to do-take some food with you, the day we were there there was thin pickings at the top-a rare thing in Japan!

I like Nagoya too for Inuyama Castle and the JR museum (train fun!); there's also Meiji Mura outdoor museum which my hayfever stopped me visiting. Also some rather lovely temples.

Have a wonderful time in Japan.