Caitlyn Jenner -- First Public Appearance at NYC Pride Event

Caitlyn Jenner let her hair down during NYC's Pride event Sunday at the Dream Hotel ... moments after the annual Gay Pride Parade wrapped.

Caitlyn arrived with a few friends and cameras in tow, apparently for her reality show, "I Am Cait."

She arrived in time for transgender actress Candis Cayne's performance.

They danced, and then Candis toasted Caitlyn ... telling the audience she was honored to know Caitlyn. She then dedicated the song, "Im Every Woman" -- to Cait, who cheered her on.