Africa

In September, it's the end of summer in North Africa, but in general it's still hot. In the Southern Hemisphere it's the end of winter: at subtropical latitudes it can still be a little cool, while at tropical latitudes, it's the end of the dry season, and there is still little rain, but the temperature begins to rise.
Where to go: Algiers, Antananarivo, Cape Town, Dar es Salaam, Gaborone, Johannesburg, Kampala, Luanda, Maseru, Mbabane, Nairobi

Asia

In September, temperatures begin to decrease in areas having a continental or temperate climate. The monsoon is still active in much of Southern Asia.
Where to go: Ankara, Astana (first half), Baku, Beijing, Beirut, Bishkek, Jakarta, Lhasa, Tbilisi (second half), Yerevan

North and Central America

Autumn starts in the countries of North America; the freezing cold returns in the northernmost areas. The temperatures are pleasant in Southern Canada and in North-central United States. It's still hot in Southern United States. In the Gulf of Mexico and Central America, it's still hot and muggy, with rains and the risk of hurricanes.
Where to go: San Francisco, Chicago, Montréal, New York, Seattle, Toronto, Vancouver, Washington

South America

In September, spring begins in the Southern Hemisphere. The rains return in the Peruvian Andes. It's the dry season in Guyana, even though it's hot.
Where to go: Asunción, Cayenne, Georgetown, Paramaribo, Rio de Janeiro, Salvador, Sao Paulo

Europe

Autumn starts; in Northern Europe the temperatures are already cool and it often rains. In Southern Europe it's still hot, and there is often a summer-like weather. In Western and Central Europe, the first half of the month is generally still enjoyable. At the end of the month, the first waves of bad weather are possible in the northern part of the Mediterranean (Southern France, Northern Italy, etc.). Around the autumnal equinox, ie September 23, the day lasts 12 hours throughout Europe (and the rest of the world).
Where to go: Amsterdam (first half), Athens (second half), Barcelona (first half), Belgrade, Berlin (first half), Bratislava, Brussels (first half), Bucharest, Budapest, Chisinau, Geneva (first half), Istanbul , Kiev (first half), Lisbon, London (first half), Luxembourg (first half), Madrid, Milan, Paris (first half), Podgorica, Prague (first half), Rome, Sarajevo, Skopje, Sofia, Tirana, Warsaw (first half), Vienna, Zagreb

Oceania

In the Southern Hemisphere, winter is ending, but the situation is more or less the same as in August: it's still the coolest and driest season in tropical islands. In Northern Australia it's still hot, but dry. In Brisbane it's still mild, while in Sydney it starts to get milder as well.
Where to go: Brisbane, Papeete, Port Moresby, Sydney