“Kaomise” (literally “face showing”) refers to the performances during the first month of the Kabuki season, which are arranged so that the theatres can show off to the best effect the actors they’ve signed for the coming year.
“Souken” means going to the theatre in a group.
Thus, “kaomise souken” is a group outing to a kaomise performance. It is not necessarily an outing by geisha; “souken” is a very commonly used term among theatre fans in Japan.
(explanation given by shirabyoshi)