What does central Tennessee mean (no intention of being snarky)? If central means Nashville area then you can get plenty of hills on the Natchez Trace and relatively safe riding and still be close to enjoying Nashville. If central means Crossville/Cookeville you have multiple options that include heading to the SE part of the state where you could base out of Maryville and ride the skyway, look rock, and plenty of other “hills” to your hearts content. Really depends on how hilly you want and how far far you actually want to drive away. No real need to go to NC
Edit: you can also head north towards the Big South Fork area and climb non stop in a very desolate area (I used to have a couple of clients - public accounting - along the KY border and those roads are lonely).