We visited HHI last year from September 16-23. We loved it!
Overall, the weather was nice. It was plenty warm enough to swim, but was not too hot to enjoy outdoor activities... highs of about 80-85. The ocean water was warm. I believe it only rained one day of our 7 day trip. The only negative was that it was pretty windy throughout the first several days of our trip, making beach outings uncomfortable (we have 2 small children and the sand was blowing in their eyes). However, the wind let up and the last few days of our trip were beautiful. (I will note that several of the locals we met indicated that the winds we experienced were rare.)
Disney's HHI resort has a counter service for food both at the resort & at the beach house, both of which were open during our stay. Harbor Cove is just a short walk over a pedestrian bridge and had several great restaurants, all of which were open during our stay. (During the summer months the Cove is host to entertainment and fireworks. These are not available in the fall. However, all of the restaurants were open.) We also drove to other restaurants on the island. We didn't find any restaurants that were closed for the season.
We found September a GREAT time to visit. The weather was still warm enough to enjoy the pool, beach, and other outdoor activities (island tour, dolphin cruise, biking, etc.)... we found MANY great restaurants... there is plenty to do, if you want to... and NO crowds (which is very different than what you'd experience during the summer months).
Best of luck with your decision!