Fall in general is great. My perception (which I’ve not validated) is October is generally wetter. That may just be from anomolies the last yew years than the actual climate, though.
Just don’t come the weekend of the Georgia-Florida football game in late October. 10,000 (newspaper’s estimate, not mine) Georgia fans flock to the island and get drunk. We’re not at all equipped to handle that many college kids all at once.