We just got home from HH and have been trying a number of the nearby restaurants on our last few trips. There are several with early dining specials and we've tried several of those. A few seem to offer the early dining year round (but , of course, that could change at any time) and several offer it on a seasonal basis in the off-season. The early menu is typically around $15 and many of the restaurants include a salad, entree and glass of house wine with at that price.
We have really enjoyed RedFish and Alexander's (these are owned by the same company and are both a short drive from the resort), Crane's Tavern (nice ambiance and menu) and Catch-22 (ambiance/menu). Kingfishers is within walking distance of the resort. Old Oyster Factory was a disappointment for us, but was OK and Crazy Crab was also very disappointing, athough several have reported a more positive experience. (We ate from the regular menu, as the early menu was very limited.)
All of these offer early dining. RedFish, Alexander's, Kingfisher, Crane's and Catch-22 all offer the glass of wine with the meal. Redfish, Kingfisher and Alexander's have been offered year round - while Crazy Crab, Crane's, Catch-22 and OOF are all seasonal (some offer the early program from Sept - Feb, others only Jan - Feb).
We have also enjoyed Scott's, San Miguels, Little Venice and Parrot Cove ( walking distance to the resort). Ocean Grille (formerly Harbour Master - and within walking distance) was OK, but a little pricey (even the early dine). Giuseppis (at Shelter Cove) is pizza place we go to each trip. HH Diner is OK - but nothing fancy at all. Mangiamo's offers 1/2 price spaghetti on Wednesday's - lots of local go there for the meal (lots of Mercedes and BMWs in the parking lot for the $5 meal -

).
We still have quite a few on our list to try with future trips (February will be the next). Our current faves are RedFish, Alexander's, Cranes Tavern and Catch-22 - all had nice ambiance, great service, nice menus and great food.
We plan to try Big Bamboo (early dine - but closed now for remodeling) and several others in the near future.