Which JR Pass to get, 7 or 14 days?

Hello. My husband and I will be arriving in Tokyo on Nov. 18, 2018 at 3:25pm at Haneda airport. We plan on going straight to Hiroshima from Haneda airport. We are deciding whether to take the plane or JR Pass to get to Hiroshima. We are not sure how long it will take using JR Pass. We plan to visit Hiroshima (Miyajima Island), Osaka, Kyoto, and Tokyo. Please advice us how many nights to spend in each city. We will be leaving from Haneda airport on Nov. 28, 2018 at 7:20pm. Any advice or opinion will be greatly appreciated. We have not booked our hotel as of yet.
Thank you so much for your time.
Felisa.

You are arriving in two months and don't have accommodation? - get onto that fast - last minute is more expensive.
How long have you had you flights/planning this trip - what do you want to see?
For Haneda to Hiroshima return the 14-day pass doesn't deliver huge savings, but might make it easier for you. It works on Japan Rail, not any of the many other companies.
My recommendation for a breakdown of days (nights accommodation) would be:
- Hiroshima - two
- Osaka - zero
- Kyoto - three
- Tokyo - three

You have 11 days, ten nights so you could add another stop somewhere interesting, or easily add a night in Kyoto and Tokyo. If you bumped Tokyo to five days, then you can easily do day trips from the capital to some interesting places.

We are deciding whether to take the plane or JR Pass to get to Hiroshima. We are not sure how long it will take using JR Pass.

You can check the time required using Hyperdia. Below is one example.

http://www.hyperdia.com/en/cgi/en/search.html?dep_node=HANEDA%20AIRPOR...

I checked off NOZOMI / MIZUHO / HAYABUSA (SHINKANSEN) checkbox since you can't take these trains if you use Japan Rail Pass. As you see all the results are using planes which is faster than slower Shinkansens (Hikari and Sakura I mean).

If you check off Airplane, you can see the Shinkansen route.

http://www.hyperdia.com/en/cgi/en/search.html?dep_node=HANEDA%20AIRPOR...

If you buy discount fare of the flight ticket it can be around 75 USD, but you can't take all the flight. As far as I checked, you can take ANA's 19:45 flight to Hiroshima which will land at 21:15 and then after 10-20 min you will take 45 min ride to Hiroshima city.

All in all I would recommend the flight because it will be somewhat cheaper and you don't need to worry for your baggage (if you have big ones). You must wait until 19:45 but you can have something to eat at the airport (actually it is not so bad at Haneda's domestic terminal with lots of selections).

After Hiroshima (2 nights I think. Hotel rate in Hiroshima is rather cheaper than in Osaka, Kyoto and Tokyo), you will take Shinkansen to Shin-Osaka and then Kyoto and finally to Tokyo. Japan Rail Pass 7 days might pay off especially if you stay in Nagoya (for example) to avoid the high rate in Kyoto. If you can get affordable accommodations in Osaka and Kyoto (which might be difficult since you will hit the peak season for autumn leaves), you might better buy single tickets (Miyajimaguchi to Tokyo normal fare and individual Shinkansen fare tickets from Hiroshima to Shin-Osaka and Kyoto to Tokyo).

6.0-6.5 hours using a JR pass with transfers.

I would just go to Kyoto first leg of your trip (3hrs. Then 1.5hrs to Hiroshima. And use the 6.0hrs Hiroshima to Tokyo as a resting day / catch up on sleep day, with Tokyo your last leg of your trip.

Hello. Thank you for the response. Is there a 3 day pass in Japan? What do they call it and where can I buy it? Or what is the website? We would like to see Mt. Fuji from Hakone, can we see Mt. Fuji without buying any tour package and just use our JR Pass? Or could you help me do a simple itinerary going to Hakone on our own with out joining the tour? With my 11 days and 10 nights in Japan, which city do you think I should include the trip to Hakone? Thank you for patience and understanding my concerns. Felisa.

You should finalize your itinerary before asking what pass to buy, because the response can change if you add destinations.

Unless you have a must reason to go immediately to Hiroshima, you could finish your tour of Tokyo first, then use a 7-day JR Pass for the rest of the country.

Example:
Day 1 - arrival, stay in Tokyo; you could buy a 72-hr subway pass
Day 2 to 4 - continue to stay in Tokyo.
Day 5 - activate JR Pass and go to Odawara, from Odawara you go to Hakone but that segment is not covered by JR Pass. Stay in Hakone.
Day 6 - Go to and stay in Osaka, JR Pass is valid from Odawara to Osaka.
Day 7 - Go to and stay in Miyajima (Hiroshima), JR Pass is valid.
Day 8 - Go to and stay in Kyoto, JR Pass is valid.
Day 9 & 10 - Continue to Stay in Kyoto. Take a day trip to Nara, using JR Pass.
Day 11 - Go back to Tokyo and airport, JR Pass is valid.

You can add a night in Hiroshima and delete one in Kyoto, or similar, etc.
Again, you need to decide what you want to do in Tokyo first, then decide if subway suits that need.
Subway pass: https://www.tokyometro.jp/en/ticket/travel/index.html

Is there a 3 day pass in Japan? What do they call it and where can I buy it? Or what is the website?

A 3 day pass in Japan? Yes there are. But they are not nation wide Japan Rail Pass. There are many types of "Rail Pass" for 3 days in Japan. For example there is JR Tokyo Wide Pass.

https://www.jreast.co.jp/e/tokyowidepass/

Japan Rail Pass is only for 7, 14 and 21 days.

http://www.japanrailpass.net/en/index.html