Originally Posted by
KI-NRT
I take it you mean Fujiya rather than Fukiya. If so, that's also a decent choice. Note, however, that there are no open-air baths at Fujiya - both the in-room onsen and daiyokujo are indoor only. Fujiya has been around since 1876, so if you're into a bit of history and atmosphere, you'll definitely get it there.
There is both Fukiya and Fujiya in Yugawara. It is a bit confusing. Here is a
link to their website. Fujiya looks to be a nice option for history buffs as well. Though they do not have in room baths.