Ken,
I grew up in the North East so I know about the winters. I don't miss them.

If it is any consolations, there are flurry's here today too but not sticking

Personally I would not spend two days in Knoxville. Maybe someone from the area will chime in knowing something more then i do about the area as i have only been there a handfull of times.
I would make my way to Deals Gap and the surrounding area's. West of Deals Gap, the Chattanooga area is nice and any road in and around the Deals Gap area is a good one.
This time of year not much is going on in the way of crowds so that is good for riding but the area interests will be limited. There is Helen GA but it is a relative ghost town during the winter months during the week. There is Maggie Valley and the Motorcycle museum there. Chattanooga has a Train Museum i believe. I have not been to it yet.