JRPass

Just listening to your goals, it does sound like it would be worth while to get the pass.

A good way to check is to look at rail schedules and fares online. A good site for this that is in English is Hyperdia (google it). Most of those distances are best done with the shinkansen (bullet train), because they're pretty far.

I just did a few quick lookups and here are the prices I came up with, all one way and per person:

Tokyo to Osaka: ¥14,250 (shinkansen)
Osaka to Hiroshima: ¥10,350 (shinkansen)
Osaka to Kyoto: ¥540 (regular JR)
Kyoto to Nara: ¥690

So, maybe not for the three week pass, but if the majority of your travels are within a 1-2 week period, it might be worth it.

Good luck :-)

Hi there!

As nighthawk663 says, it may not be worth a 21 day pass (¥57,700). Here's the full ticket price for your itinerary (prices may differ slightly from nighthawk's because of time of day etc):

1. Tokyo > Osaka: ¥13950, (194mins, 556km)
2. Osaka > Hiroshima: ¥10150, (104mins, 345km)
3. Hiroshima > Kyoto: ¥10990, (126mins, 380km)
4. Kyoto > Nara: ¥690, (45mins, 41km)
5. Nara > Kyoto: ¥690, (44mins, 41km)
6. Kyoto > Tokyo: ¥13420, (161mins, 513km)

TOTAL: ¥49890 for 6 legs

As you can see, the basic ticket price for the legs you mention come in at less than the cost of a 3 week pass, so I cannot recommend this option. If you were to fit your long distance travel into 2 weeks however, you would make a good saving of  ¥4790 per person, and would have the added convenience of totally free additional JR travel within those 2 weeks. For mega savings, if you manage it all on a 7 day rail pass you'd save even more over individual tickets, (¥21,590), but it really depends on the pace of your travels.

You can also use the rail pass on all JR trains in Tokyo. (Here's a map of JR lines in Tokyo for reference).

Hope this helps!