There are very few geisha in Tokyo. In thirty years of traveling there, I have seen exactly one. The geisha are not prostitutes, although they are usually "kept" by a wealthy man, and for foreigners, a geisha party is likely to be boring, since their shtick is to flirt with the guests (in Japanese, of course) and perform traditional songs and dances to the accompaniment of traditional instruments.

The only place you're going to see geisha performing in public is twice a year in Kyoto, where there are two extravaganzas per year, the Miyako Odori in April or so, and the Gion Odori, which I haven't seen, at some other time. If you go to the Pontocho area of Kyoto at night, you may see geisha and maiko (geisha-in-training) walking around.

If you want to see kabuki (all-male theatre dating from the 18th century), that's considerably easier. The Kabuki-za is right near the Ginza, and they sell one-act tickets for foreigners, complete with rented headsets that narrate the action in English. (An entire play goes on for hours and hours, and if you're not into Japanese theatre, one act is plenty for enjoying the action and the costumes.)