There have been several good threads about packing for HHI. First, I believe the kitchens are virtually the same as fas as untensils, dishes, etc.
Secondly, packing for a beach vacation is definitely different than packing for a WDW resort. For us, we plan our entire meal thing differently. When we go to HHI we really only do one, or at most two, meals out at restaurants, usually dinners. We have also learned not to bring too much since there is a supermarket just down the street.
Essentially, we bring some easily packable breakfast stuff, snack foods, water bottles, etc that we buy in bulk at our local warehouse (Costco / BJ's). Other than that we make a run to the Piggly Wiggly the first day and pick up ther perishable things like bread, deli, bagels, fruits, milk, juice, etc.
For us, breakfast is always in the room. For lunch, we tend to make sandwiches and/or eat at one of the resort's snack bars. For dinner we do take-out and eat in our room, or at the beach.
Folks will have different preferences. Some refuse to spend anytime in the kitchen on vacation, others take advantage of the bazillion restaurants in HHI, others will cook every meal and avoid the time to get ready and sit in restaurants, etc. Only you know what works best for your family.
Other than the food options, think about the beach. You may want to bring your own umbrella and chairs, (though you can rent them on the beach from the lifeguards,) many bring bikes, fishing equipment, golf & tennis stuff, etc. I've even seen some folks bring their own canoes, kayaks, & boats.
There was one great suggestion for a portable screen door since the balcony doors do not have screens, though I lost that thread. If you need to use the pull-out sofa for sleeping, some folks prefer bringing an air matress instead.
Regardless of what you packed - or dont' pack - rest assured you'll be able to find anything you need at the myriad of stores within a 10 minute drive of the resort