You are aware that Bermuda is located approx. 650 miles east of the Carolina coast.....and isn't anywhere near the warmer Caribbean ??..has a SEMI-tropical climate ??...and may not be the best destination at Christmas / New Year for a typical '..island / beach..' sort of vacation, right ?? Check out the Climate Averages for December / January for an idea of Air & Ocean Water Temperatures to expect--
http://www.weather.bm/data/climatology.html
Bermuda's climate at this season of the year is usually grand for golf, tennis, and general touring...but not necessarily '..beach weather..'...though heated pools are usually okay.
Bearing this all in mind, and the varying personal preferences, priorities, interests, etc of the members of your family group, you should probably be looking at the larger, full-service hotels and resorts (pools, spas, restaurants, activities, etc)--FAIRMONT HAMILTON PRINCESS; FAIRMONT SOUTHAMPTON HOTEL; ELBOW BEACH HOTEL; GROTTO BAY BEACH RESORT. A few smaller hotels might also serve--COCO BEACH RESORT, SURFSIDE, HARMONY CLUB, GRAPE BAY BEACH or perhaps ROSEDON or ROYAL PALMS. There's one other often overlooked small hotel (some people are a bit put-off by it's 'faith-based' reputation)--WILLOWBANK HOTEL & RESORT...but the downside to this place is a relatively remote and somewhat inconvenient location. But i f "..bang for the buck.." is a high priority, then GROTTO BAY RESORT tends to offers the best priced, off-season '..packages..'.
http://www.fairmont.com/hamilton/
http://www.fairmont.com/southampton/
http://www.mandarinoriental.com/bermuda/
http://www.grottobay.com/
http://www.cocoreefbermuda.com/
http://www.surfsidebermuda.com/
http://www.harmonyclub.com/
http://www.grapebay.com/
http://www.rosedonbermuda.com/
http://www.royalpalms.bm/
http://www.willowbank.bm/index.asp