Aeration on Bermuda greens, which pretty much everything in the Pinehurst area is now, including all the courses you mentioned, is in the late spring or early summer. There might be some small tine/top dressing stuff after that, but it won’t interfere with play much, if at all. But aeration schedules are typically done pretty far in advance, and a call to the course might well get you an exact answer.
As to the time of year, the fall is ideal golf weather in the SE. The grass hasn’t gone dormant, the greens are perfect, the temperatures moderate, and you avoid the issues with summer thunderstorms in the afternoons. (The only qualifier to that is the remote possibility of a tropical storm coming thru.)