Beyond that, OC is not distinguished from CC in Tennessee law and therefore follows the same rules. Don't carry it into a courthouse or on school property (if you're a non-student adult, you can store it unloaded in your vehicle). If you carry into a place that serves alcohol, don't consume any alcohol while there. If you go to any local parks, check for postings at the entrance; local governing bodies are allowed to ban weapon possession in their parks. These should cover state prohibitions. Of course, don't carry onto Federal property, like a Post Office. You may carry in national parks, however.
Also, be sure to watch for postings whenever you go into a business or other establishment. Establishments are able under Tennessee law to prohibit weapon possession on their property; and, if properly posted, these postings carry the weight of law in Tennessee (Class B Misdemeanor). To be properly posted, an establishment must have one of two sign types: (1) a sign containing prohibition language that is "substantially similar" to the statute, or (2) a gunbuster sign containing the traditional circle slash with a gun in it. To be "substantially similar," the sign must (1) state that weapons are prohibited, (2) state that the prohibition is made pursuant to the authority of Tennessee state law, and (3) state that a violation is a criminal offense. If either sign ("substantially similar" language or the gunbuster) is present at the entrance, then you may not legally carry in that establishment. Proceed with caution regarding places that are posted but not properly, such as having a sign that just says "no weapons allowed" without having the "substantially similar" language or gunbuster (officially, I have to recommend you don't carry these places either).
Let me know if you have any further questions.
Disclaimer: I am not a lawyer. Nothing contained in this message is, or should be construed as, legal advice. I accept no responsibility for any actions you may or may not take based on this information. For legal advice, consult an attorney.