Another vote for HHI.
Food/Drink
While the resort has limited options, the whole island is brimming with superb restaurants, bars, pubs, diners, etc. Unlike WDW which touts exceptional dining (only it often isn't and you pay a premium price on top of that), HHI offers great food at mostly acceptable prices, and most of these places are easily accessible from the resort, some within a 5-10 minute walk, in fact. Also unlike WDW, you don't have to wait until the crack of dawn a couple of months out to make reservations and hope for the best. Most can be reserved via a dining app and except for particularly busy times, reservations aren't difficult to get. Now, some local joints don't take reservations, but if you go early to these places, you can usually get in without too long of a wait.
Activities
As mentioned above, you can bike nearly everywhere on HHI as the trail system is both extensive and safe. You can rent bikes from the resort itself, though only once you arrive, so if it's a busy season, there might not be any to rent. Conversely, there are several reputable bike rental companies on the island that deliver to the resort, and you can book those ahead of time. Meanwhile, the resort itself does daily activities such as tie-dye t-shirts, making pillows, or creating wreaths. There are yard games located throughout the serene and lovely grounds of the resort such as bocce ball, giant checkers, corn hole, horse shoes, basketball, and a small putting green. You can fish or crab from the pier, take part in pool games, or just sit and drink on your balcony that will either overlook the interior of the resort, the pool, or perhaps even the marsh/channel. Of course, there are many things to do at HHI, in general, with day trips to Savannah or even Charleston.
Beach/Pool
While the resort sits a mile and a half away from the beach, it's a great beach--wide, soft, easily accessible. You can drive to the beach, take the free Disney shuttle, ride your bikes, or even walk. The Beach House also has a pool and private access to/from the beach. Many bike over and hang out at that pool, stroll the 50 yards or so to the beach and hang out there a bit, then come back to the pool, grab a drink, etc.
Overall, a visit to DHHIR is meant as one of pure relaxation, a true break from the constant go-go-go most people experience at WDW. There are plenty of Disney touches along with the best CMs anywhere. I'd give it a shot.