2-week itinerary (+ Cherry blossom advice?)

Hello! Next year will be my very first time visiting Japan. I am staying 14 nights late April - early May. Here is what I have so far, and I need help rounding out the last few days of my trip:

-Tokyo (4 nights)
-Hakone (1 night in ryokan)
-Kyoto (5 nights - with day trips to Nara, Osaka, and Himeji)

We will leave Kyoto on April 28th or April 29th, which leaves 2 last nights in Japan before heading back to Tokyo to fly home. So it seems there are a few options:
-Head west to Naoshima art island (1 night) and Hiroshima/Miyajima (1 night)
-Head north to Kanazawa (1 night) and/or Takayama (1 night)

I know they both offer different things, but I really would like to know what people think!
LASTLY, if there's any chance of seeing cherry blossoms on our way out, please advise. I know we are visiting pretty late but it would really make the trip to be able to see it. We'd likely have to go further north - any ideas? :)

https://www.japan-guide.com/e/e2011.html

Look like if you go north of Tokyo, you might get to see some Sakura.

https://www.japan-guide.com/e/e2011_when.html

Looking at the table of dates above. It you got to Takayama (on your list of maybes) first up. So like arrive, one night in tokyo, then go to Takayama on your second day. You may just catch some also.

Cherry blossom blooms in the northern Tohoku or the southern Hokkaido from late Apri to early May. See "Pic de floraison (moyen)" in the below.
https://fr.wikipedia.org/wiki/Front_de_floraison_des_cerisiers#Dates

However, these dates are the ones for city centers. If you go into mountains, you could see cherry blossom in a more southern area. Mt Yoshino in the south Nara is such an example. The peak in the Oku-Senbon area could last until 1 May in the coldest year.
http://www.town.yoshino.nara.jp/kanko-event/%E5%90%89%E9%87%8E%E5%B1%B...
Takayama is also in a mountainous area. This page lists the past records of the first blooming date. It could take about a week to reach the peak. So, the peak could be as late as 28 Apr.
http://kankou.city.takayama.lg.jp/2000002/2000638/2001083.html

As in the above, there is a huge yearly variation in the peak date. If you really keen to see cherry blossom, it would be better to cover the route between Hokkaido and Tokyo. One of the examples is to fly in Kansai, then fly to Chitose, and take a train back to Tokyo to fly back to your home. You could fly in Tokyo, but an open jaw would be more efficient. Hakone could be done from Tokyo. Note the Golder Week will be 28 Apr to 6 May in 2018. It would be better to stay in a city during that period to avoid crowds.
https://www.timeanddate.com/calendar/?year=2018&country=26

In April, a sunny day could be comfortable in Tokyo, while a cloudy day could be chilly. I would choose a warmer season to visit Kanazawa and Takayama. If I visit Hiroshima, I might think of flying in Fukuoka.
Tokyo https://www.benricho.org/weather_ratio/13_04.html
Kyoto https://www.benricho.org/weather_ratio/26_04.html
Hiroshima https://www.benricho.org/weather_ratio/34_04.html
Kanazawa https://www.benricho.org/weather_ratio/17_04.html
Takayama https://www.benricho.org/weather_ratio/21_2_04.html

Sorry for the typo.
https://www.japan-guide.com/e/e2282.html

Thank you, Hakata and Louis! First, I think I will re-order my trip so that I am in Tokyo during Golden Week, and not any other tourist destination. Maybe from there I could do a daytrip up north to see some sakura in Seido or Hirosaki. I will look into the options.

In Tokyo go to Ueno Park and Shinjuku Gyoen - both will have some cherry blossom. The "main" season in my experience runs about six weeks. For a bit more I collected some information for late viewing on a page http://japancustomtours.co.nz/sakuraforecast.htm For more serious and impressive displays, heading north of Tokyo is a good idea, even just to Sendai (2 hours north of Tokyo) gives some good locations.

You will not have the big displays that would normally occur around the start of April, but there will still be enough trees with good blossom. I even had some nice photos this week in Tokyo of cherry blossom (along with about 100 other people enjoying the hanami), but that is typical for that particular group and type of tree.

When I looked at your itinerary I was surprised by how little time you are actually spending in Kyoto itself. If you like temples and shrines then you might want to add two more nights there.

On the other hand, if you'd like to see a small city with a fabulous garden and nice castle, plan for two nights in Kanazawa. Don't miss the World's Second Best Melon Pan Ice Cream (https://www.tripadvisor.com/Restaurant_Review-g298115-d7851339-Reviews...)

IMHO either take the two nights and spend them in Kyoto, or cut a night from elsewhere and take 3 nights to do either of your options.