I would recommend the Simpson Bay Area:
Close to the airport, restaurants, and some shopping
Mary's Boon Beach Resort. Quirky, small, but nice place, right on the beach. The restaurant is okay but nothing to write home about. The staff are fabulous.
Also in Simpson Bay on the smaller side, Horny Toad Guest House.

Away from the beach in that area:
Bakers Suites
Liberty Inn

Mid January tends to be easier to find rooms.

I can tell you where not to stay: The timeshare sellers' happy hour.