If you're willing to spend 2.5 hours in a train each way (only cost would be your time since you have JR Pass), I might suggest taking the yamagata shinkansen all the way up to kaminoyama onsen, then spending the day at the Koyo Hotel/Ryokan. I visited them in Feb this year and it was amazing (and snowy): ¥10,000 for sukiyaki meal, ¥11,000 for shabu shabu meal.

What you get for your money is a day-use room (10.30am - 3.00pm), in-room kaiseki, and free use of their two onsens. What my wife and I did was reach at 10.30, go onsen, have lunch, relax, then onsen again (they switch the Male / Female assignments over lunchtime), then leave.



More pictures of their onsen on their website: ??????????????? ?????????

Skip to 7m15s for short video on the meal (no onsen videos/photos obviously :P)


I don't think they have any private onsen option though, but as you'll be alone I'll assume that you don't really need it. Plus the baths will likely be almost deserted anyway.