7 days Japan Rail Pass

Hi! My family of 5 (including 2 kids + 1 senior citizen) will be traveling to Japan this December. Our plane tickets are already purchased and tentative IT as follows:
Dec 29: Arrival at Narita at 13:10hrs, then proceed to Osaka
Dec 30: Osaka tour
Dec 31: Osaka (explore by ourselves)
Jan 1: Daytrip to Kyoto
Jan 2: Daytrip to Kobe
Jan 3: USJ
Jan 4: Osaka to Tokyo
Jan 5: Depart from Narita 13:55hrs and back to home
Please please advice if we will need to purchase a 7-day JR pass for this. If that is economical or if there are other passes that would be better.
I'd appreciate all the help. Thank you!

"IF" you go to Kobe using the Shinkansen, the pass will just pay off.

It would've been better to have purchased a multi-city flights instead, arrival in Kansai and departure at Narita. But since you already purchased them, it's ok to stick to your itinerary. How about change the day of Osaka exploring by yourselves to one more day to Kyoto? Kyoto has a lot to see, and one half day trip won't be enough. Or you could do Nara instead, since it's close by.

I forgot to say that you could join both osaka days into one. During the day you could do the tour and explore the city at night, which is pretty safe. And also fun with all the lights at Minami area.

Agree with the above but I would trade both Osaka days for Kyoto and Nara. Unless you are really into big cities, in which case trade a day of Osaka for a day of Tokyo, which has way more options for things to do. Of course if there is something you really want to see in Osaka, then spending a day there is perfectly reasonable, but my opinion is basically that for sub-2 week itineraries spending any decent amount of time in Osaka is rarely worthwhile, and that Kyoto and Tokyo are usually better.

With your Itinerary, the 7-day rail pass works and would be my choice. Ifm sure you know that you can purchase the JR Rail Pass Order only from outside Japan. Then convert your Order to the Rail Pass at JRfs Service Center at Narita Airport. The Service Center will issue tickets only to your 1st destination city. Day 1 starts on your arrival date Dec. 29 with the last date of use being Jan 4, the 7th day when youfll arrive in Tokyo. FYI, the train ticket from Narita to Osaka cost about 17,400Yen compared to less than 3,300Yen from Tokyo to Narita. So, your 1st day of Rail Pass usage on Dec. 29 is better.

Then, on Jan 5, pay for transportation to Narita Airport since the travel cost is comparatively low. You have the choice of using 2 train lines or 3 bus lines. You may need to catch a taxi from your Tokyo stop to your hotel and again for your return commute to Narita. Consider your Hotelfs location in Tokyo relative to the train or bus stops. This will be a good research exercise for you to look for the best choice. Also looking into Adult, Kids and Senior fares. Additionally, with the rail pass you can change your day trips and deviate from your itinerary. If this is your 1st trip to Japan, youfll be back. If not the 1st, youfll still be back. Have a wonderful trip.

Thank you @hakata14 for the reply. We've changed the IT. We will be going to Hiroshima instead of Kobe (and just research where we can eat Kobe beef in Osaka :))

Thank you @catiasmteixeira for the reply!
Really? We can just explore Osaka for 1 day? My concern is the kids really want to visit the Aquarium and I'm thinking, this might take up half a day already. Based on my research, seems there is really more to see in Kyoto..hmmm... I'll have to read up on this more. Thank you again for the insight!

The aquariums will require more than half a day. Holiday period, big lines and queues just like weekends.

Thank you @LIZ for the reply!
Yes, I'm now considering of perhaps spending either 1 day more in Tokyo or Kyoto, instead of the add'l day in Osaka. I just have to find a way to schedule everything that both the kids and the adults would be happy :) Either way, my 7day JR pass would still be worth it right?

Thank you @Harold for the reply! I appreciate the detailed explanation on the passes. Will definitely do that. And yes, this will be my 3rd time in Japan, our 1st on the Kansai area as both times we were just in Tokyo and then to Yuzawa Niigata. We just cannot get enough of going there! The country is very beautiful and there are still so many places to visit that once or twice is never enough :)

The next time, if your last City is Tokyo as for this trip and your last Rail Pass day is Jan. 4 to Tokyo and, paying from Tokyo to Narita, you can spend 1 or 2 more days in Tokyo. The same can be said if you make Yokohama your last stop, spend a few days there and catch the direct Narita Express from Yokohama to Narita. Then, instead of 7 nights in Japan, you can spend 8 or 9 nights and still use the 7-day Rail Pass.

This is what wefre doing next month with our 1st stop in Yokohama via NEX and activate the Rail Pass on the 3rd day with our last stop in Toyohashi before going to Narita Airport using the Rail Passf 7th day.
In the alternative, you can pay for the train/bus tickets to your first stop in Tokyo or Yokohama and activate the Rail Pass 2 or 3 days later. Then, on the last Rail Pass usage day you can head back to Narita from Nagoya, Toyohashi, Shizuoka, etc.

Get the seven day Japan Rail pass and you could also get the 14-day N'Ex return ticket which will save time on arrival, and you can do the voucher exchange the following day. A seven day pass will give reasonable (not spectacular) savings.
@Harold is wrong as you can buy the national rail pass in Japan (on arrival at Narita for example), just it costs an extra ~10%.
You will need to be careful with travel across the New Year period as some days and trains will be fully booked.

JapanCustom Tours should have said that there is a recent change per www.quora.com that in part says: Until March 8, 2017, you cannot purchase Japan Rail Passes in Japan. You must purchase the rail pass before you enter the country. You also must have a temporary visitor status (landing permit or tourist visa), or proof of permanent residency overseas (if you are a Japanese national) to redeem your voucher once you get into Japan. Afterwards, as part of a trial basis you can also purchase the JR Pass at select Japanese airports and major train stations, although at a higher price.
This is not the most current Japan Railways Group policy. Still this is good information to update us about buying JR Rail Pass. The article also said the higher gin Japanh price is 15% that may in fact be 10% now but not available to Japan RESIDENTS..

For buying the JRP in Japan, the change back in March 2017 is hardly recent, and you can buy the pass while in Japan and have it delivered if you don't want to pay the extra - I do it all the time and get them delivered to me here in Tokyo. I think the problem is relying on a Quora source (secondary or tertiary) rather than a primary source for information. Even some psuedo-official sites get information wrong.
There were a few minor changes for eligibility in the last couple of years (for Japanese citizens living overseas), but the basic requirement remains being a temporary visitor and that proof is affixed to the passport on entry into the country - which is why you need to present your passport when exchanging the voucher for the actual pass.

There are a couple of passes/discount tickets available to residents with a non-Japanese passport, like the N'Ex return ticket, and sometimes the eligibility requirements (like for the Japanican discount eVoucher) are buried in fine print.