Have 3 extra days in Japan. Please advice

We will be in Japan from March 25th to April 7th 2018, flying in and out of Narita. We have planned about 5 days in Tokyo and 4 in Kyoto. That still leaves us with 3 free days. Please advice what other places I can visit or things that can be done in these 3 days. We are a couple with a teenage daughter. Thanking you all in advance.

This totally depends on your interests and what you want to experience.

You could visit Hiroshima and Miyajima, or Mt Fuji/Hakone area, or Kanazawa/Takayama area, or you may consider a stay at a temple like Koyasan, or even spend more time in Kyoto and explore nearby towns like Nara, Osaka, Kobe, Uji and Hikone as day trips.

Too many options. What are your interests?

Thanks for your advice. Yes we would love to see and experience a few new places. So surely wouldn�ft mind staying over in Hakone or MT Fuji area for a night too. Would it be a good idea at that time of the year?

What is your proposed itinerary for 12 days?
Is Kyoto right after Tokyo and the 3 missing days are at the end, or are they in the middle between the two?
Will you be considering a visit to Universal Studios in Osaka while in Kyoto?

The Hakone area has more to offer than just viewing Mt Fuji which is very weather dependent (i.e. cloud forecast should be less than 20%), mind you some of the activities there such as the ropeway or the cruise maybe closed if the weather is bad. There are onsens and ryokans (traditional Japanese inns) there too, if you like to experience that.
So if you want to go for the experience, staying a night in Hakone could be an option.

Lake Kawaguchiko is closer to Mt Fuji, and the nearby area has Fuji Q theme park. It also has ryokans with onsens. Gotemba Outlets are not far away from either.
So you can consider a night stay in each of them depending on your interests and budget.

search info about them in this site to get a better idea of what appeals to you best and use hyperdia or google maps to estimate travel time between your destinations.

I would add a day to Tokyo, (so you have more time to add Fuji/Hakone) and 2 days for Hiroshima/Miyajima.

You are travelling in the cherry blossum peak season. So I would make a decision quickly and book early so you don't miss out.

Thank you so much for all the ideas. Yes we are doing kyoto right after tokyo. And the 3 days are towards the end.