Hakone Ryokans

We will be visting Hakone next month. Have looked at the list of Ryokans but cannot decide which one to pick. Any recommendations for a good one. thank you very much

Can you state your priorities/preferences - budget, room type (Japanese or western), good onsen/good view?, food served in-room or at the restaurant, etc.....

Also, if you can mingle with other naked guests in onsen (gender separated, most common, large, indoor/outdoor) or kashikiri(time reserved private, sometimes free of charge) or in-room private(outdoor, hot tub size)for just for two(?) of you. The rate goes up & the onsen tub become smaller respectively unless you pay a lot at some specialty ryokans.
It all depends on your budget.

...which we really enjoyed, Lalaca at Gora. Very reasonable, big rooms, great food, and very good onsen (with private onsen), and the people are lovely. There is a website, it doesnt really do it justice though. Pretty handy spot too, about a 5 minute walk to the train/cablecar. The japanese/english rooms with the bath are enormous and great value, we put our kids in that one and took the japanese room next door which was quite big as well.