January and February are definitely part of the winter-getaway High Season in the Caribbean; but demand isn't as high as during Spring Break.
If your kids are tots not in school yet, Club Med Punta Cana in the DR has Petit Club Med with programs for ages 2 and up. (Note that registration and a fee are required for ages 2 and 3.) And Beaches resorts offer baby care and nurseries.
- continue to Chinese New Year Celebrations