Best Hot Spring in Hakone with Mt. Fuji view?

I will be staying in Shinjuki and will obtain my Hakone Freepass in Odawara the morning I go to Hakone-Yumoto.

Since I will be doing all of the exciting things in Hakone, and some point I want to go to a hot spring (of course, right?) but I want one that will have a nice view of Mt Fuji while I relax there.

What do you suggest?

There are surprisingly few onsen with views of Mount Fuji in Hakone. The following one can be enjoyed by both staying and non-staying hotel guests:
http://www.hgp.co.jp/language/english/sp/

Maybe Hotel Green Plaza Hakone

http://traveljapanblog.com/wordpress/tag/hakone/

Thank you very much!

They allow non-guests to swim between 12pm-3pm.

How would you suggest I fit this into my full-day Hakone-tour?

Thank you!

It is located half way through along the typical Hakone round course, along the Hakone Ropeway. If you do the typical round course, you are likely to pass the hotel during the baths' opening hours:
http://www.japan-guide.com/e/e5210.html