food/first onsen trip

http://www.oizumi.ne.jp/~sennin/
^ I read an article in which a top Tokyo chef recommended this eatery since the owner forages, shoots, and sources all of his own food which is sometimes quite novel according to the article at least.

But this place is pretty far from Tokyo so I thought I would get your advice on this one. But before that, I also wanted to ask about visiting an onsen for the first time while in that part of Japan. In the links section, of the eatery's website is a link to this "pension house". (whatever that means)

http://p-albion.jp/?cat=640
So, I called them up and inquired about the area and the eatery. My Japanese is not good but from I got she said that eatery is in a very remote location and the closest hotel would be this place:
http://www.ryokan.or.jp/inn/50720

Next, I asked her about the best onsen in the area and she recommended this place:
http://panoramanoyu.sakura.ne.jp/panorama.htm

But I asked another guy I knew about some places and he sent me this link:
http://onsenguide.org/oyu/yamanashi/hokutoshi/konyoku.html

These seem to be mixed gender onsens but unless I am missing something they don't seem to be worth it at all from the pictures. I looked through all 16 of them too.

http://p-albion.jp/?page_id=17
This seems to be some kind of instructions on how to get in the area but I am still confused at how I should best exactly get to this eatery and the onsen as well. Thoughts?

well the pictures look pretty decent. The hotels are located in nature. As for location, trains seems to be a good idea.
On how to choose a hotel, it truly depends on the person. It is subjective. Occasionally there is a best hotel, but usually this is up to a person's personal preference.

So all in all, take a train (or drive). Check in hotel. Ask the concierge to make a reservation for you at the eatery. Go eat.

Quick question if anyone sees this in time, if I visit the onsen first then the restaurant, if I return to the onsen will I have to pay the entrance fee again? Or do I only pay once a day?

Most onsen do not have in/out privileges so you would typically have to pay again.

Update:
The onsen only charged a one-time fee that was good all day. Very convenient!