If you are looking for an all-inclusive resort with reasonable airfares from Chicagoland, your best bets will be in Punta Cana, Dominican Republic, or the Cancun/Playa del Carmen area. Both have everything on your list, except perhaps wild life, depending on how you define that. You can get cheaper flights into Cancun, and there is a wide variety of offerings once you are there. If you don’t think you want to leave the hotel much, then stay in the Cancun hotel district or along the Maya Riviera nearby. But if you want to interact with a real and lovely town, then stay in Playa del Carmen or over on Cozumel. There are many nearby activities and some very interesting ruins.
There are a lot of possible places that might work for you, so it’s hard to narrow my suggestions down without knowing where you are starting from and how far you are willing to travel from there. But two things that come to mind are Bali, Indonesia, and the Cancun area of Mexico. If you are in the US or Canada then it will obviously be a long flight to Bali, but things are quite cheap once you get there so it’s really worthwhile. The island has beaches and water sports, but also really interesting culture, not to mention loads of shopping and beach resorts. Its main problem these days is vehicle traffic, so getting around the island is slower than it used to be.
Fortunately, it rarely rains at all in Cairo, so even though December is one of the wetter months, that means nothing and you are unlikely to see even a drop of rain. Hotel prices do reach their peak in Cairo starting late in December, so it's best to go early in the month if possible. Egypt is definitely one of the cheapest places to travel in December, and the weather is surprisingly nice as well.
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.
The 17th-annual Hilton Head Island Motoring Festival and Concourse d’Elegance takes place Oct. 26-Nov. 4, attracting automobile enthusiasts and all who enjoy the southern charm, splendid fall weather, and extraordinary classic cars. The Hilton Head Island Oyster Festival (Nov. 9-10) is an oyster extravaganza with live music, crafts, a Kid Zone, and sports lounge. A stay at the Inn and Club at Harbour Town at the Sea Pines Resort will provide luxury and comfort in low country style. Or book a home rental through Vacation Company. 
The subtropical climate of Hong Kong means that summers are particularly hot and wet, and spring is warm and humid. November is the sweet spot, with clear, sunny days and mild temperatures. During your trip, you'll want to take a traditional junk boat ride on the harbour (seen here) and check out the sweeping city views from Victoria Peak, which you can reach by tram. Another can't miss? Stockton, a hidden speakeasy-style whiskey bar in Central.
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