My husband and I try not to live close to anything. Our last place was 2 hr from a town with more than 1,000 people.
With that said, I think it would be "safer" living closer to the CDC. The reason is, they know what they are dealing with. How many illnesses are misdiagnosed because the local Dr's have never seen them before. They don't really know how to handle extreme situations. In the town we lived in, there was one Dr, in one clinic, with one nurse. They were overworked during normal flu season, I can't imagine if there was some sort of contagious outbreak.
Granted the CDC is a government agency, so bureaucracy is involved. However, there are also leading specialist and experts on rare and not-so-rare diseases.