The three places that jump out to me are the Playa del Carmen area just south of Cancun in Mexico, the island of Puerto Rico, or Costa Rica. All of those have endless beach activities and sights and great food and everything else, and they are all well within your budget. Puerto Rico would be easiest, and probably my first choice. Costa Rica is better known for adventure activities that might suit the younger ones. There are several good resort areas along the Pacific coast that would work.
Located off the coast of East Africa, the Seychelles—an archipelago consisting of 115 islands—is about as close to paradise as you can get. Crystal clear water, lush jungles, and powder-fine sand make it the ultimate early winter escape, particularly for romantic getaways. Book one of the 30 breathtaking pool villas at Six Senses Zil Pasyon, which is among the region's top luxury resorts. The hotel is situated on a private island that offers prime territory for snorkeling, sailing, kayaking, and hiking—plus, the spa has scenic pavilion-style treatment rooms that are worth the trip alone. Health conscious guests will be particularly impressed by the property's new "Eat with Six Senses" program, which is intended to make travelers leave vacation without the guilt that comes with overindulging. There are four tailor-made treatment plans that focus on sleep, detoxing, fitness, and more, depending on the issues you prefer to address.