When you get to Tokyo, each of you should buy a Suica or Pasmo stored value card. You just tap this in and out for each ride and don't have to worry about whether it is the railroad or the subway you are riding on.

Here's the math on the JR pass: Kyoto-Tokyo is Y13,500, the train from KIX to Kyoto is Y3,000 and the Narita Express is Y3,000 -- this totals Y19,500, and a 7 day JR pass is Y28,000. You won't spend even 1/3 of the difference on JR in Tokyo (and there is no JR service inside Kyoto).

Furthermore, there are ways to save on the costs of all three trips. The coupon shop I mentioned above is only one possibility. As but one additional example, the Keisei Skyliner will take you to Narita airport from Ueno just as fast and is Y1,000 cheaper (plus I've even seen Keisei Skyliner tickets at discount in a coupon shop). However, with only 6 days, it might not be worth it to spend time trying to figure all that out.