Most shopping is closed on Jan 1st, but plenty of places will still be open.
Most of Odaiba is open on Jan 1st (I'm personally no longer a fan of Odaiba, but...).
Soramachi complex at Sky Tree should be open on Jan 1st.
Typically all Seibu-related stores (Sogo, Pepe, Emios) have been open on Jan 1st.
There is not much in the immediate vicinity of the IC Tokyo Bay, and it is not the most inspirational high-end hotel. But it is fairly convenient to HND, and you can also take the river boat ("suijou bus") back from Asakusa to right near the hotel.