Hi Lucia,
I think that you would be fine with a 7 day JR Pass and activate it on the day that you travel to Nagasaki or Hiroshima.
The Suica card is also valid in Osaka, so you can simply keep using it - if you do buy it in Tokyo. The Suica card for Kansai is called ICOCA. You can also buy that if you don't have a Suica but want one for in Osaka.
Nikko is also a great itinerary stop, either as a day trip from Tokyo or as an overnight stay. The trip is covered by the JR Pass and it makes sense to travel there using it, because otherwise it can cost over 10,000yen for a return from Tokyo!
Nagasaki is well worth your time, it's a beautiful town with history (such as Dejima). The town is build on the side of a mountain overlooking Nagasaki bay, this results in some beautiful sunsets.
Lastly, what I would do with 17 days in Japan? Probably stick around Kyushu and Shikoku for most of time, both islands have much to offer but are a little of the beaten path. I would probably visit Beppu for a good onsen, go to Aso for hiking and enjoy a sunset all the way south in Kagoshima while watching Sakura jima blow it's ash in the wind. Around Shikoku I would visit Matsuyama Dogo spa to relax, go to Kochi to enjoy the palms on the beach and lastly head to Matsuyama to take the ferry to Naoshima before heading home. Oh and if I had time sneak in a visit to Kinosaki Onsen.
Let me know what you think :)
Daniel