Correct Hanna. Quenya was the language the elves used in Valannor and that Feanor brought to Beleriand when he left. In Beleriand he came across Sindarin, the Grey-Elven or Noble tongue spoken mainly by the people of Thingol and Melian. From then on Sindarin was the language of choice in common speech. Quenya was reerved for formal farewells, such as Namarie; special occasions, such as coronations; and spells and records, such as Saruman's weather spell spoken atop Orthanc. The people of Numenor as well as the Dunedain and Gondorians also kept Quenya in reserve for special ceremonies and occasions. There are also a few other elven languages such as Telerin, but these two are the main ones.
As for a separation of language due to region, I know that two different forms of Sindarin were spoken in Middle Earth, basically one for the Western half and one for the Eastern half, but if I'm correct the main differences lie in the stresses, pronunciation, and spelling.
For more Tolkien Language help, visit:
www.ardalambion.com
Or, thumb through the Silmarillion and etymologies.
~Scott