As I just shared in another thread- I live in Beaufort County (same county as HHI). September and October are absolutely gorgeous times down here. I would think the full complement of water sports/activities should be good-to-go in September. You may get lucky in October too- but in general October/November is probably better thought of as "golf season". Beyond water sports- the weather in general should be very pleasant. We've had multiple Thanksgivings in the 70s in recent years. Heck- Christmas this year was downright tropical. Should work out well for you in Sep/Oct. Frankly, January through early/mid February ("cold" by SC standards and wet) is the only time I'm not all that "bullish" on HHI weather.
As far as things to do near the resort. Yes- tons! Boating, fishing, shopping, golf, fine dining, high quality cultural offerings (plays, musicals, orchestras) etc. all in the area. Bluffton, Savannah and historic Beaufort all nearby- and very fun/interesting too.
Enjoy the Lowcountry!