I haven't actually come across Kortirion in UT, Beleg.
Tirion is a city built by the Vanyar and Noldor when they first came to Valinor. It was originally the city of Ingwe, but after the Vanyar departed to be closer to Manwe, it became the city of Finwe and later Finarfin.
I'm not too sure about the early works of Tolkien as I'm still trying to decypher HOME, but there is mention of Kortirion in the Book of Lost Tales. In these books, which contain some of Tolkien's early workings of what would become the Silmarillion, the world is viewed through the eyes of a human mariner named Eriol. He discovered a strange island and was taught many things by its inhabitants who were faerie.
In this version Kortirion is a town built by the returning Noldor on Tol Eressea because they could not return to Valinor. I'm not sure from this early working whether Kortirion and Tirion itself are actually the same city or not.
In these early works, by the way, Tolkien seems to be founding his world of Middle Earth in the real world, and Eriol was a human from our world who met the elves. Tol Eressea is still the same island used by Ulmo to transport the Elves to Valinor, but in this version he moves it back to Middle Earth once more in order to transport an army of Elves to face Melkor. When he tries to move it back West once more, part of the island snaps off and becomes Ireland. The bulk of the island becomes Britain, with Kortirion in the present position of Warwick.
Obviously, Tolkien made many changes over the years and Eriol never made it into the Silmarillion. As I mentioned, Kortirion may have evolved over time into Tirion.