JR pass worth it for 5 day trip out of Tokyo?

I will be traveling to Japan with my family, (we are 4) for 12 days. We will arrive to Narita and stay in Tokyo for 4 nights, then go to Hakone on day 5 and spend the night there. After this we want to go to Kyoto, Nara, and Osaka, but what we are having trouble with is deciding whether we should stay in Kyoto, or stay in Osaka and just commute to Kyoto on day 6. Ideally we want to take one day to see Kyoto, and the next day to see Nara and Osaka. Would it be a bad idea to commute from Osaka to Kyoto and Nara? Everything in Kyoto is either booked or super expensive, and Osaka has much more options and more reasonable prices.. After these two nights we will travel to Naoshima and stay there one night, then go back to Tokyo until the end of our trip. My other question is, for this itinerary do you think a JR pass would be worth it?

It can be - it is not only a matter of time, it is the distance traveled and if the 7 day pass pays off.
With the trip to Naoshima, you do more than break even.

Staying in Osaka is not a big deal - it's only about 30 minutes by rapid train to Kyoto. Nara is about 50 minutes and 800 yen. Just one day in Kyoto is seriously shortchanging the place. You could see Nara Park in half a day and give Kyoto at least a few more hours.
http://bit.ly/1Rhxg0E
You can also add more in if you are willing to get up earlier. The Fushimi Inari Shrine is open 24/7 and you can avoid the crowds by going early in the morning or evening, plus the Honganji Temples open around dawn and the Kamo Shrines are also open with the early bird.