Wunderlust would have lots of suggestions. here are some of mine

September is OK in Kenai peninsula, but starts getting cold going inland.

In fact, Denali NP would have drawings for the slots that let private cars drive inside park, I think starting Sept 15 each year. You can find info on the NP website.

Cruiseship season shuts down after Sept 15. So the lodgings would be a lot less expensive, though some B&Bs also shut down.

Sightseeing cruises also would drastically reduce their schedule after mid September. Ditto tour operators (bear viewing, flight-seeing, trips to Glacier Bay NP, that kind of thing).

I believe rental cars operate year-round in Anchorage. Though most on the Southeast of Alaska (only reachable by boat or seaplanes), most rental car operations are seasonal. For example, Avis on Skagway closes after Sept 15.

With that in mind, you would have to plan your time of travel around that.