Assuming you are going all the way across NE, there is a beautiful garden in Omaha (and many museums, Old Town, and more) all most likely already decorated for Christmas. There was a story in Midwest Living magazine about the garden, tho. If I find it, I'll post later with more info.
If you are into watching the scenery roll by, we really enjoy driving I-80 across NE and WY. There are some intersting museums between Omaha and North Platte, too, but not sure if they are year round. Surely there will be info at the rest stops on the I. Or find the NE tourism website.
Being more familiar with the west end of the state, and with the WY section of I-80, don't overlook the small towns, especially the last three in NE. There are some nifty western clothing and housewares, as well as Sierra clothing specializing in winter wear, stores in Cheyenne, both on Lincolnway, and on the Interstate on the east end of town. The WY capitol complex is intersting, with museums, etc. There is a buffalo ranch south of town, which I believe invites people to tour, but don't know the details.
Have fun, and may you enjoy good weather and roads! Fall in this part of the country has been long and beautiful, so it may end abruptly any day now.
mrj