The beach and ocean water were way too cold for us this past January. No one was out there. There is a strong cold wind that blows. Also the points are higher. I wouldn't do Vero in January again, especially with a 12 year old.
I say VWL or Boardwalk. Saratoga is my favorite for a non park visit, but I like the spa and the pools, and the proximity to retaraunts. For your son, there is AMC and splitsville, bike rentals, horseshoes, usually pool games and things at community hall. Not sure if there are video games? I am pretty sure there are at BLT in Community Hall.... we were just at BLT last month, but I didnt think to look.... I think BLT might be a little boring if the weather is cold. At VWL you could always go to fort wilderness and rent bikes, hoop de doo, fishing, etc.