Aloha from Kaua'i!
September is a beautiful month here normally.....I'm sure you'll have a great time!
As far as "activities".....while there are tons of activities here that people pay a lot for, and enjoy very much.....we have just as many wonderful "free" activities to enjoy that won't cost you a dime.
The beaches here are all free and open to the public....from Ke'e Beach and all the way west out to Polihale State Park you will find amazing vistas of beach and ocean, many of which you can swim at (always check daily ocean conditions wherever you go) and enjoy the amazing ocean....the way you feel when you are immersed in the waters here is something I can't explain.
Kaua'i is the oldest of the main Hawaiian islands, and our scenery is more dramatic IMO due to the erosion that has occurred over all those years......whether you are a casual stroller or a more experienced hiker, being on a trail up in Koke'e Park/Waimea Canyon, Nounou Mountain (aka Sleeping Giant)...part of the Kalalau Trail, or any other of our myriad hiking trails.....will give you vistas that you will not get from any boat or helicopter....in my opinion there is nothing like actually "being there" as opposed to viewing something from a distance away.
If you want to do one, or many of the high priced "activities" that we have here, I'm sure you will enjoy that as well......but I just wanted to say that in my opinion....trite but true....the "best things" in life here on Kaua'i are absolutely free!
So don't stress so much about booking those activities or the best restaurant on island right now....take your time and do some research on the island itself and what speaks to you....then narrow it down to what you really want to spend your time and money on.....September isn't as busy as month as it is now for instance, so you have some time.
But don't be like some people I see myself who visit here and who run from one activity to another, one fancy restaurant to the next....never really taking the time to "see" the island and experience it. This is a laid back, slower paced island.....and you'll be missing out if you don't also slow down and enjoy it!
I know you will have a wonderful time here.....here's wishing your research on this beautiful place is fun and rewarding and that your vacation exceeds your expectations!