September has advantages. The kids are back in school, and the number of holidaymakers (Irish and overseas) is much reduced, but the season is not completely finished. So you can get the best of everything: most seasonal things are still available, and the pressure on accommodation, restaurants, and attractions is reduced. For such reasons, it is a time of year Herself and I like to target for recreational trips.
In my mind, I associate October with rain. I could be wrong.
Read my views with caution. I live in Ireland, and that can distort my perceptions as well as inform them.