osaka, kyoto, hakone, tokyo

Your itinerary does not say how many days in each city so it's hard to give you advise.

But because Narita-Tokyo alone costs about $40, I like to schedule my stay at 13 or 14 days so it will cover my Narita Express.

In Tokyo, use JR as much as possible so you can use your pass.
But should experience Japanese subway once. So many new subway lines nowadays that I can be complicated.

Have fun!

Hi there!

Looking at your itinerary I think the best way to travel would be to buy normal train tickets.
A JR Pass is amazing if you travel between a couple of regions in Japan, for instance a return Tokyo - Kyoto will quickly pay off. Your itinerary consists of just one way Kyoto - Tokyo with a stop at Hakone (which is directly on the route).

A JR Pass would work very well if you traveled from Tokyo to Osaka and made the itinarary above but for now I would recommend going for normal tickets. What is nice to know is that children below 12 pay half price and children below 6 are free of charge. Some conditions apply, you can read more about traveling on the JR with children here.

I hope this helps!
Daniel