JRPass

Hi there,

Yes, the Japan Rail Pass will get you to Nagasaki from Tokyo. Here's a sample itinerary for you. For Unzen you should aim to get to JR Isahaya station, and from there take the non-JR Shimatetsu bus to Unzen. Here is a timetable for the Shimatetsu bus (look at the second table for Isahaya to Unzen). 諫早駅前 is JR Isahaya Station, and 雲仙 is Unzen. Buses between these places leave roughly every hour and will cost ¥1,300 each way.

There are also cheap flights in Japan between Tokyo Haneda and Nagasaki that you should look into if you are only intending to visit Nagasaki.

We have a blog post on the benefits of Green Car (1st class) for JR Pass holders that you may find useful.

Hope this helps!