I live in Knoxville and worked in Oak Ridge for many years.
Have you been to Oak Ridge? If not, you might find the housing situation ... interesting. The rather large core of the original town has no HOAs. Not aware of any zoning restrictions on antennas, but you will want to contact the city codes office to verify. Or engage a real estate buyer's agent to find out for you.
Those houses were all built during WW2 for Manhattan Project workers. By and large, they are good houses. Well-constructed and most neighborhoods have been kept up well. But the floor plans, if still original, are strange by modern standards. E.g., the front door of most houses opens into the kitchen. And other oddities. But the yards are generally tiny. Good for towers and verticals. Not so much for dipoles, rhombics, etc.
In recent years, a number of new neighborhoods have been built as the government sold surplus land. The older they are, the less likely they are to have HOAs. But the most recent neighborhoods are pretty much the McMansion type with very restrictive HOAs. But that is no different than really anywhere else in the USA.
So. if you want an historic wartime house, you should be fine. Recent suburbia-style house, think flagpoles and other stealth antennas. OR is an extremely patriotic area due to the nature of the work conducted there so flagpoles are no problem.
Think carefully before moving to OR. It's not for everybody. Some people move there because they like the schools but work in Knoxville or in Blount or Loudon counties. A lot of people work in OR, but live in Knox/Blount/Loudon or in Harriman, Clinton, Kingston, or Oliver Springs. Shopping isn't good unless you are happy with Home Depot and Wal*Mart. Dining is also sparse. Your fellow residents will be, by-and-large, scientists and engineers plus atomic trades union-types that do the dirty glow-in-the-dark type work at Y-12 and the Lab. And retired, metastasized (in more ways than one) versions of the same.
You can still get acreage for your dream antenna farm nearby, but it won't be inside Oak Ridge or Knoxville.