Hi there!
Sounds like a great trip! For a 7 day rail pass to be worth it you'll need to spend over ¥28,300 on individual tickets. Lets take a look at the legs you mention, and then see if adding day trips makes it worthwhile:
- Narita airport terminal 1 > Ueno: ¥2940, (81mins, 82km)
- Ueno > Osaka: ¥13750, (212mins, 560km)
- Osaka > Kyoto: ¥540, (29mins, 42km)
- Kyoto > Osaka: ¥540, (28mins, 42km)
- Osaka > Kobe: ¥540, (28mins, 42km)
- Kobe > Osaka: ¥540, (28mins, 42km)
- Osaka > Kansai airport: ¥3140, (57mins, 64km)
TOTAL: ¥21990 for 7 legs
The base cose of the travel you list means that in it's basic form it will not be worth purchasing a 7 day rail pass.
For day trips, I really recommend a trip to Nikko from Tokyo if you can make it, and if possible an overnight stay in a Japanese hot spring (onsen). As you have 2 days free in Kansai towards the end of your trip, how about an overnight stay at Kinosaki Onsen. It's around 3hrs from Osaka, but is a fantastic little town with many Onsen, a great atmosphere and routinely described as the best Onsen town in the area of Hyogo. Here's a good forum post with more, and you can also book many onsen online.
If we include these day trips into your itinerary, the value of a japan rail pass becomes a little more clear:
- Narita airport terminal 1 > Ueno: ¥2940, (81mins, 82km)
- Ueno > Nikko: ¥5230, (115mins, 146km)
- Nikko > Ueno: ¥5230, (111mins, 146km)
- Ueno > Osaka: ¥13750, (212mins, 560km)
- Osaka > Kyoto: ¥540, (29mins, 42km)
- Kyoto > Osaka: ¥540, (28mins, 42km)
- Osaka > Kobe: ¥540, (28mins, 42km)
- Kobe > Osaka: ¥540, (28mins, 42km)
- Osaka > Kinosakionsen: ¥5450, (160mins, 183km)
- Kinosakionsen > Osaka: ¥5450, (170mins, 183km)
- Osaka > Kansai airport: ¥3140, (57mins, 64km)
TOTAL: ¥43350 for 11 legs
If you choose to do these day trips I would certainly recommend a 7 day rail pass over separate tickets.
The trip will have a mixture of normal JR trains and Bullet trains, making travel interesting! You can look up exact train timetables, types and costs at the Hyperdia travel planning website and learn how to use Hyperdia for Japan Rail Pass holders through our video blog.
Hope this helps!