The first linguistic maps in the world date from the 1800s, and in the first few decades, these were maps of individual words.1
The large language families are in bold
face.
Indo-European
Most of Europe, Iran and India
Sino-Tibetan
Most of China and Myanmar
Afro-Asiatic
North Africa and the Middle East
Altaic
Turkey, Azerbaijan, Kazakhstan, Turkmenistan, Uzbekstan, Tajikistan, Mongolia and Manchuria (debatably, Japanese and Korean)
Niger-Kordofanian
Sub-saharan Africa
Malayo-Polynesian
Malaysia, Indonesia, other Oceania, Taiwan and Madagascar
Uralic
Finland, Hungary, Latvia, Estonia and certain people of northern, climactically challenging Russia
Dravidian
Southern India and Sri Lanka
Caucasian/Kartvellian
Georgia and the Caucasus Mountains
Nilo-Saharan
Squished between Afro-Asiatic and Niger-Kordofanian
The Daic Family and the Austro-Asiatic Family
Daic is for Thailand, Austro-Asiatic for Viet Nam and Cambodia
Xhoe
Southwest Africa
Basque
Northeast Spain and Southwest France
Pama-Nyungan
Australian Aboriginal
Note: All the maps on this page are from Professor Boeree, who is not a linguist, but did come up with a fairly complete set of maps closely following what I gather is the general consensus among linguists.