Best Rail Pass Solution?

Hi! I'm entering Tokyo first, exploring there for about 5 days, then travelling to Mt. Fuji, spending 2 days there, then to Kyoto, followed by Osaka, (probably will spend about 3-4 days exploring here) then onto Hiroshima and finally Nagasaki, before travelling straight back to Tokyo. I'll be in the country 21 days in total. I may take a trip up to one of the lakes in Hokkaido before or after doing the above trip. Will the JR Rail Pass be the best option for me in this case? Thanks!

definitely. although you don't really need it for tokyo and mt fuji so you could just get the 2 week pass. if it was me i would go for the 3 week.

you can use the pass from the airport to tokyo (n'ex). this is worth about 3000yen, then to fuji is a few thousand yen and you can use the pass around tokyo (but only on jr trains not the subway) so a mild inconvenience.

what lakes in hokkaido?

If you go to Hokkaido, I recommend to fly there. For example:
Tokyo - (train) - Kyushu - (air) - Hokkaido - (air) - Tokyo

For the one way train trip between Tokyo and Kyushu, a 7-day pass would come cheaper, but a 14-day pass and especially a 21-day are likely to come more expensive than regular tickets.

I honestly dont know yet, Joseph, what lake(s) I'll visit. I guess I'm kind of limited to ones near Sapporo for ease of access, but further research is needed I think :) I would love to visit Daisetsuzan National Park, but accessibility seems to be a bit of a problem...

Instead of going from Nagasaki straight to Tokyo, I would first visit Kyoto before going to Nagasaki and stopping over at Osaka on your return to Tokyo. The train trip from Nagasaki to Tokyo is about 8 to 9 hours. Break this same day train travel time in half by stopping over at Osaka. This is not an issue if you decide to fly from Kyushu to Hokkaido.

Unless you've been there before and if time permits, you should consider visiting Hiroshima and Miyajima Island. A short sightseeing of Himeji Castle would also be a plus.

Since you're spending the first 5 days in Tokyo and possibly may fly from Kyushu to Hokkaido and back to Tokyo, either the 7 day or 14 day JR Rail Pass may work to your benefit. If you do a detail day by day itinerary and decide if you'll fly from Kyushu to Hokkaido, you will be better able to assess your train travel requirement and if the 7 day or 14 day Rail Pass works for you.

Have a safe and wonderful trip.