Africa

In June, the summer begins in the Northern Hemisphere; the Atlantic coast of Morocco is sunny, but it can be foggy in the morning, and the sea is cold; in the Red Sea the weather is definitely too hot; the African monsoon advances northwards from the Gulf of Guinea.
In the Southern Hemisphere winter begins, and even at tropical latitudes it can be a little cool. In Mauritius it can be a little cool, and there can be wind and some rain.
Where to go: Canary Islands, Cape Verde, Comoros, Madagascar (north), Mayotte, Mozambique (north coast), Seychelles, Tanzania, Zanzibar

Asia

The monsoon by now affects most parts of Southern Asia, but the dry season begins in some parts of Indonesia.
Where to go: Bali

North and Central America

The hurricane season begins in the Gulf of Mexico, and also in the Pacific coast of Central America; however, hurricanes will be more likely in the following months.

Caribbean Sea

The heat is muggy, the rains are heavy, and the hurricane season begins, although they will be more likely in the months ahead. If you want to go to the Caribbean, you can choose the Leeward Antilles (Aruba, Bonaire, Curacao) and the Venezuelan islands, which are generally sheltered both from hurricanes and heavy rains.

Mediterranean Sea

It's the beginning of the summer, with sunshine and warm weather throughout the Mediterranean Basin. The sea is still a bit cool, especially in the French coasts and in the Alboran Sea, and in the north (France, Northern Italy, Slovenia, Croatia) some disturbances can still pass.
Where to go: Algeria, Cyprus, Egypt, Greece, Israel, Italy (center and south), Lebanon, Malta, Spain, Tunisia, Turkey (west and south coast)

South America

Winter begins in the Southern Hemisphere: at sub-tropical latitudes it's cool or even cold. The waters of the Pacific are cold, up to tropical latitudes, and fog and low clouds are common along the coast. In the north of the continent, in the Northern Hemisphere, it is summer, and heat and rain prevail.

Oceania

The winter starts in the Southern Hemisphere, which means that there is a wide choice, among the islands that lie at tropical latitudes (but not too far to the south), where you will find sunshine, little rains, and a pleasantly warm weather, tempered by the breeze.
Where to go: Australia (Darwin), Cook, Fiji, Hawaii, Nauru, Niue, Papua New Guinea (Port Moresby), French Polynesia (Tahiti, Bora Bora), Solomon Islands, Samoa, American Samoa, Tonga (north-central), Wallis and Futuna