As for dining, there are two restaurants right near the Peppertree on Money Island that you should include on your dinner list. Amos Mosquitos' and The Island Grille.
The Island Grille is where the locals go. It is very small and casual, but you will want to make reservations. The food is incredible and they have a BOGO special on Tuesdays (I think). You will want to find out for sure and make your reservations... you will still be willing to go back and pay full price once you have eaten there, it is THAT good.
Amos Mosquito's also has some great weekday specials that can make it a bargain too, and there the food is also very good. The service here is top shelf, but it maintains a casual, fun feel.
These are the only places on Money Island near the Peppertree that I would choose. Just across the bay there are many choices in Moorehead City and they will be adequate, but the better food will be 5 minutes further down the road in Beaufort. The Blue Moon Bistro attracts people who come in from Charlotte... it is also small and a bit more upscale. Aqua is right near by; it is very good too, but a bit more expensive and more of a chic and trendy approach. Although very good, we liked Blue Moon best.
Most important when dining in the area is to choose restaurants that participate in "Carteret Catch". They support the local fishing industry and serve fresh local catch items on their menu. Most often they will have a "Carteret Catch" sticker on the door, or a sign posted.
Avoid The Channel Marker... there are simply too many other outstanding places to choose from that I've named.