I assume you have a carry permit.
TN honors all other states' permits, but you must have one to conceal OR open carry.
In general, you can open carry in most places; you may get some looks of course. A LEO can ask to see your permit at any time. I go a month at a time without seeing anyone open carrying, so it's not real common, but then I don't get out much
Anyplace that is posted with gunbuster sign or certain wording (many aren't correct but best to honor those signs anyway) are no carry of any kind, and though we've not found anyone actually charged yet, it IS a specific misdemeanor for doing so. Besides the issue of intoxication while packing, you cannot consume ANY alcohol in a public establishment while packing.
Cades Cove is part of the National Park, so like all National Parks it's okay to carry there (but not in federal buildings on park property, which are supposed to be posted).
What else? Schools of any type, including colleges, NO. City and county buildings must be posted just like private biz. Municipal parks are some yes some no, the no's are posted. A few attractions, like Dollywood, are posted, most aren't. Most restaurants aren't.
That's about it, I think. Have a great stay!