Africa

In December, it's winter in the Northern Hemisphere, so the heat is found only at tropical latitudes. In the countries of the Sahel and south of the Sahara, it's usually the best season. In the Southern Hemisphere it's summer, and in general it's hot in Austral Africa; in many areas the rainy season begins, and cyclones are possible in the Indian Ocean.
Where to go: Abidjan, Accra, Addis Ababa, Bamako, Cape Town, Conakry, Dakar, Johannesburg, Cairo, Lagos, N'Djamena, Nouakchott

Asia

By December, it's winter; it's very cold in continental Asia; in the south, the winter monsoon brings rainfall in the exposed slopes, for the rest at tropical latitudes the sun prevails. Sometimes late cyclones can occur in the Philippines and in Southeast Asia, especially in the first half of the month. You can go in southern cities, where usually it's warm or hot and it doesn't rain.
Where to go: Bangkok, Dhaka, Doha, Dubai, Ho Chi Minh City, Karachi, Kuwait, Mecca, Mumbai, Muscat, New Delhi, Phnom Penh, Taipei, Vientiane, Yangon

North and Central America

It's winter and it's very cold in Canada and in North-central United States; sometimes, cool air masses can move southward, to the Tropic and beyond. To play it safe, it's better to go down in latitude.
Where to go: Guatemala City, Mexico City, Havana, Miami, San José, San Salvador, Santo Domingo, Tegucigalpa

South America

In the Southern Hemisphere, in December it's summer, so it's typically hot and rainy at tropical latitudes, and even at temperate latitudes it can be hot. Along the Pacific Coast, the sun shines and the temperature is not too high.
Where to go: Lima

Europe

It's the first month of winter in Europe. On December 21, the winter solstice, it's the shortest day of the year. In Mediterranean countries, the weather is often still autumn-like, that is, mild, but also with possible periods of bad weather.

Oceania

It's summer in the Southern Hemisphere, so at tropical latitudes the weather is hot and muggy, with heavy rains, and the passage of cyclones. In the Northern Hemisphere some tropical cyclones may still pass, at least in the first part of the month. The Australian Outback is on fire, while in the south of the country the weather is usually warm but not too much, even though sometimes the wind from the desert can cause waves of scorching heat. The best season begins in the cooler New Zealand.
Where to go: Auckland, Wellington