In Teplitz (Bohemia) in 1812, though this has not yet been proven beyond any doubt. But the chance for another date and place is very, very, very little indeed. The most important research on this problem has been done by Unger, who published his discoveries in 1909 and 1911, later on confirmed by Sonneck. More and more evidence was found, the newest, as far as I know, in the sixties and the seventies, thanks to the investigations by Plevka and Racek, thoroughly discussed by Goldschmidt in 1977, whose book on the identity of the Immortal Beloved is still a must for every researcher.
Sonneck, O.G. The riddle of the Immortal Beloved. (New York, 1927).
Goldschmidt, Harry. Um die Unsterbliche Geliebte. (Leipzig, 1977).