Indeed it is your choice to base in any city.
You can do the sequence of Kyoto-Nara-Osaka or Osaka-Nara-Kyoto. Osaka or Shin-Osaka is the main station of various limited express (Hamakaze or Konotori) bound for Kinosaki Onsen. There is also the infrequent Kinosaki limited express which starts from Kyoto that will traverse via Northern Kyoto (where Miyazu is). Each limited express ride travels for 2-3 hours.
see atleast a waterfall or beach enrouteI do not know if you have searched on this but Ishikawa (where Kanazawa is) faces the Sea of Japan. Noto Peninsula is 2 to 3 hours away from Kanazawa.
I also found this link if you want waterfall when in Kanazawa
https://www.tripadvisor.com.ph/ShowUserReviews-g1021240-d1424222-r2244....
From Awara Onsen which is few stations away from Kanazawa, you will see the Tojinbo Cliffs facing the Sea of Japan.
You'll get the view of Biwako or Lake Biwa as you seat on the left side of Thunderbird from Kanazawa going to Kyoto or Osaka.
In Osaka, you can see the waterfall in Minoh Park.
Amanohashidate faces Sea of Japan. For sure Northern Hyogo where Kinosaki Onsen is faces Sea of Japan as well.
Kinosaki Onsen Station to Tottori Station is 90 minutes away, if you have heard or known the Tottori Sand Dunes.
I am not saying that you visit them all since you are time-constrained. It's always your decision where do you plan to see the beach or any body of water en route.
I am not sure about your travel on 'wet/chilly that time of the year'. Are you travelling on spring time or last quarter of 2017 or year/s to come?
Anyway, since you will end up in Tokyo prior flight home, it makes more sense to do the Odawara or Atami to Shimoda travel as you prefer before settling in Hakone.
If your flight time permits you to relax in Hakone, maybe you can catch the NEX trip from Kawaguchiko
http://www.eki-net.com/pc/jreast-shinkansen-reservation/english/wb/com.... Check here the bus schedules from Gotemba to Kawaguchiko
http://bus-en.fujikyu.co.jp/route/detail/id/1/. If not, you can always go back to Tokyo then train or limousine bus to NRT.