Tokyo - Yuzawa - Tokyo - Nagano- Tokyo - Hakone- Osaka- Kyoto - Osaka. You don't have to get back to Tokyo after you visit
the Yuzawa skiing resort (in Niigata Prefecture) or
the so-called snow monkey park (in Yamanouchi Town in Nagano Prefecture).
Also, when you start from Tokyo, usually Osaka is further than Kyoto.
You can travel
by JR Shinkansen lines
from Tokyo Station via Takasaki to Echigo-Yuzawa Station
then via Takasaki to Nagano Station
then via Joetsumyoko to Kanazawa Station,
and from Kanazawa by JR conventional (= non-Shinkansen) lines
(on a Limited Express Thunderbird) to Kyoto Station,
and from Kyoto by JR Kyoto Line
(on a Special Rapid train) to Osaka Station.
A 7-day Japan Rail Pass is valid for 7 consecutive days,
and you will have 9 calendar days from the 10th to 18th of February.
To make the pass cover your way to Kansai Airport [KIX] on the 18th,
you should use it from the 12th or later day;
when you use it from the 11th,
you should pay additionally for your KIX access.
I suggest you make a combination of
a JR EAST Pass (Nagano, Niigata area), JR regular tickets and a Nankai discount ticket
for your major legs
(other than the legs Odawara City -- Hakone Town and Nagano City -- Yamanouchi Town,
which are not covered by any JR pass).
This combination covers (almost) all the JR train rides for your currently-planned trips,
and the total amount is estimated at most at 29410 yen (except for Uji and Nara trips),
which is about the same as the price of that 7-day (Ordinary-Class) Japan Rail Pass.
The JR EAST Pass (Nagano, Niigata area)
can be used on any 5 days during the 14 days from the day of issuance,
and it covers
the (Tokyo Monorail and) JR sections
on your ways from the airport (NRT | HND), to Echigo-Yuzawa and to Nagano
and the JR section until Joetsumyoko on your way to Kanazawa.
A foreign tourist can purchase an Exchange Order for this pass
at 17000 yen through the JR East website (set up separately for booking passes).
- A JR EAST Pass (Nagano, Niigata area)
https://www.jreast.co.jp/e/eastpass_n/The amount of the JR regular fees for the JR route beyond Joetsumyoko until Osaka
is estimated at around 11000 yen,
on the condition that you don't stay overnight on your way for Kyoto.
For you to get from Osaka City to KIX,
a Nankai Kanku-WEBTOKU Ticket is available at 1130 yen.
A voucher for this ticket can be purchased
only through the Nankai website (set up separately for sales of discount tickets).
This discount ticket allows you
to have a Nankai Limited Express Rapi:t train ride from Namba Station to Kansai-airport Station.
Seats in a Rapi:t train require reservation;
you can try to reserve your seat when you turn in the voucher for your ticket.
-[Dep:Namba/Arr:Kansai Airport] KANKU-WEBTOKU TICKET (regular seat)
http://www1.nanka-e-tabi.com/NEREN/ItemDetail.aspx?tc=IB4AOSNAMKIR&sk=...
