I love the Biltmore. Even getting into the fundraiser/gala season when every single non-profit and corporate America company hosts every function imaginable here, I never get sick of this place.
Do yourself a favor and talk with a willing staffer about the history of this place, I think they may do tours but I'm not sure. I worked here for about 3 minutes in early college years and the best part of that experience was the history lesson. They had a speakeasy!
What I love most is going to the lobby bar and ordering something special depending on time of day and company; on a recent Saturday afternoon with a girlfriend we shared a bottle of wine (from the cafe) and last winter it ranged from a Manhattan to a decadent dessert and cup of coffee or glass of Port. Then, I go out back to the courtyard. (This is best on a chilly evening when the fires are all lit.)
And I just sit, relax, watch all the pretty people and pretend like I'm on vacation.