Fujinoya Ryokan is the most traditional ryokan in Hakone but we cannot stay in there because of renovation to 2020.
Another one, I recommend you Ryuguden which is traditional and gorgeous. In addition, we feel japan traditional atomosphere and good scenery.
Finally, Many hotel and Ryokan, have traditional and good mood, are in Hakone.
I suggest you to select the Ryokan on location base, Motohakone, Yumoto and Kojiri.