Onsen recommendation near Jigokudani

I am looking for onsen ryokan near the monkey park, nice (but not expensive spa) outdoor hotbaths, japanese dinner & breakfast experience (not just noodles), private toilet is nice, but not a deal breaker.

The absolute closest onsen ryokan you can get is the Korakukan
http://metropolis.co.jp/tokyotravel/tokyoworldtravel/393/tok...
which you can book through www.japaneseguesthouses.com

I have stayed there and while it is a bit shabby in spots, the food was great and the monkeys were...everywhere. You have to hike a bit to get in to it, there are other more modern ryokan that are closer, but it's neat to have the monkeys walking around on the roof and getting into the bath.

Is the walk to Korakukan (I hear 20 minutes) doable with rolling luggage?

I went to Korakukan three years ago...based on conditions on the trail then, I wouldn't take rolling luggage. It's only slightly uphill, but it's gravel or dirt, not paved. I was there in the winter and the path was muddy in a few places. I don't know what it would be like in summer.
There may be way to have the ryokan come get the luggage...it seems like they must have a cart or ATV for getting their own supplies in. I don't know anything about that though.

Outside winter, you can drive almost to the door of the ryokan. The parking area is less than 5 minutes from the ryokan. See the map on the following page:
http://www.japan-guide.com/e/e6025.html