>>1046233>>1046194 Here...I like museums, history, and "pedestrian streets" kind of neighbourhoods.
Bechtler is good, museum wise,
http://www.bechtler.org/Museum of the new south is also good, for what it is.
NASCAR Hall of Fame is fine if you are into Uddn-uddn at all.
Ben Long frescos are worth seeing if you are walking by -- I'd not make a special trip just to see them, but if you are passing the buildingon foot, look in the lobby of the Bank of America or TransAmerica buildings uptown. (My uncle is one of the people in the TransAmerica painting.)
http://www.visitnc.com/story/ben-long-s-frescoesWe're not well-populated with pedestrian street neighborhoods, though Uptown is very walkable though Urban. Also look into NoDa as a walkable artsy/nightlifey area.
http://www.noda.org/I am not a fan of the Mint Museaum, but some folks are.
Not sure what their winter hours are, but Reid Gold Mine is the site of the first Gold Rush in the US when Citizen Reed realized the big shiny rock he was using as a doorstop was in fact a 17 pound gold nugget.
http://www.nchistoricsites.org/reed/Raptor Center north of town does rehab on birds of prey in need of some love, not strictly natural but the birds are neat.
http://www.carolinaraptorcenter.org/Nature would best be found by heading up tot he mountains, it's about a two hour drive to get into mountain country.
I also appreciate some natural beauty, if it's not far away (although I'm not sure if it's possible in winter).
Hope that helps some.
Oh, and if you have any interest in the NFL or BA, both will be playing in town in December -- whether your visit matches a home game I'll leave for you to look into.