In the Shelter Cove area which the Disney resort is there are many great restaurants...Scotts Fish Market (Seafood), Ela's Blue Water Grille (Steakhouse) and San Miguels (Mexican).
In Sea Pines ($5 fee to get into that area) you can visit the Salty Dog Cafe which is a fun touristy must do place.
Coligny Plaza - Bomboras Grille...great food and service...outdoor seating and live entertainment...one of our favorites.
Now, I have never been to the area during the winter months...only summer. Just returned from a trip to HHI (at a different resort) and we spent most of our time on the beach or at the pool. Therefore I cannot recommend excursions.
We have stayed at Disney several times and can tell you not once was a room ready earlier than check in time. But we loved the low key laid back atmosphere of the resort.
I owned at DVC Hilton Head for many years. Went for Easter break a few years in a row. We got tired of the often cold Easter week weather so we stopped going.
With that said, I hope you are prepared for cooler weather. I would immagine New Years will be cold (low 50's probably). Unless I am skiing, I hate being cold on vacation but it might not bother other people so much.
I always requested a marsh view room. You could also request a pool view room. The two bedrooms attached to the lobby are all lock-off (I believe).
If you have never been to this DVC room, you are in for a treat. I love the property and that time of the year, it is a benefit not to be on the ocean.