I agree with Clew In...September probably won't be a good time to kite but it is a great time to be in TCI...no crowds and better deals on accommodations. RWI (Royal West Indies) is probably one of the best/affordable places to stay on Grace Bay yet it is situated a little far from the shopping and dining you'll find in the vicinity of the Regent Grand or Salt Mills Plaza. If you don't plan to kite or site see, staying in the Regent Grand area is where I'd suggest so you won't have to rent a car...check on vrbo.com.
We always stay at RWI. Here is a photo from a few years back kiting right there. Usually too offshore there so I head over to Long Bay. Need a car for that though.
The wind angle is better towards the Regent and Grace Point for Grace Bay kiting.