Jenny,
We just came back from HH. There's plenty of food on the island, all accessible to you since you will be driving. Most of the restaurants were open when we were there, although some of the hours were shorter than in season. Your best bet is to call ahead of going to be sure they are open. When you check in at HH, you'll receive a booklet of restaurants and their menus, a list of restaurants where
DVC members get discounts, and another dining guide. Some places will even deliver for a fee.
The snack bar at the resort, Tide Me Over, was open from 9 a.m. until 2 p.m. while we were there. It's good for breakfast and lunch. Signals, the snack bar-restaurant at the Beach House, was open from 11 a.m. to 3 p.m. We had lunch on the patio overlooking the ocean and we were the only ones there. Snacks and some food is available in the resort store, the Broad Creek Mercantile, which was open from 8 a.m. to 6 p.m.
One night when we didn't feel like going any where, we ate an early dinner at Scott's Fish Market, which is in walking distance from the HH resort, and watched the yachts sail by. Kingfisher's also is in walking distance -- in front of the entrance to the resort, but we didn't get a chance to try it. There are many, many excellent restaurants, family style to fine dining. You certainly won't go hungry!
If you go for your anniversary, I recommend having "A Private Affair" at the resort. Chef Gordon will prepare a gourmet meal for you in a Grand Villa. My DH and I did this in celebration of our anniversary while we were there this week, and it was wonderful.
Enjoy,
KMarie