Hi there!
It's a little hard to pin down your exact costs as I'm not sure where you're staying in Izu - do you have any ideas on places you intend to stay in the area?
Assuming you'll stay around Mishima, here is a rough cost estimate for your tickets:
- Narita airport terminal 1 > Shinjuku(jr): ¥2910, (84mins, 89km)
- Shinjuku(jr) > Yugawara: ¥4060, (80mins, 113km)
- Yugawara > Kyoto: ¥11870, (168mins, 444km)
- Kyoto > Yugawara: ¥11340, (179mins, 414km)
- Yugawara > Odawara: ¥320, (16mins, 15km)
- Odawara > Yugawara: ¥320, (17mins, 15km)
- Yugawara > Mishima: ¥400, (24mins, 21km)
- Mishima > Yugawara: ¥400, (18mins, 21km)
- Yugawara > Shinjuku(jr): ¥4060, (83mins, 113km)
- Shinjuku(jr) > Narita airport terminal 1: ¥1450, (100mins, 86km)
TOTAL: ¥37130 for 10 legs
As you can see, as a 14 day rail pass is ¥45,100, your only chance for savings here is with a 7 day pass. Looking at your costs, your best chance of using more than the ¥28,300 cost of the 7 day pass is from Shinjuku > Yugawara > Kyoto > Yugawara, however even then the JR ticket cost will still be borderline the same as a 7 day rail pass at ¥27270.
If you do go for a 7 day pass for this period, you'll have the flexility to change your plans and visit other places and towns as you wish, and also any further travel on JR during this period would be free (for example a day trip to Hiroshima from Kyoto). In the end though , I think whether you should go for the rail pass will boil down to how much extra travel you think you'll make.
Hope this helps!