REWARDS - Respect
Drive to the Caligula's casino. Follow the croupier, but don't get too close or you'll spook her. You also fail the mission if she gets too far away. She stops at a sex shop, so hurry inside after her. She's somewhere inside, but just go in the red marker to trigger a cutscene. After that happens, get inside the east room and pick up the gimp suit, then go back outside and continue following the croupier, remembering not to get too far or close.
Park outside the croupier's house. The guy she was talking to before will walk down the street (he is not marked on your map). He is a bit on the old side and is wearing no shirt. Kill him and pick up the purple object he drops. After that, head inside the girl's house. Watch the cutscene and then the mission will end. Respect earned.
Note that you will have to court Millie Perkins before she will give you the keycard, which is required in order to move onto the next mission. There are two ways to do this, with the first one involving actually dating her. To easily get her status above 33%, get the gimp suit and head to her house. If she's home, then you will go inside, have your little "date" with her and then be done. Doing this twice will get you above 33%, which will have Millie call you and let you get the keycard from her house.
The other method of obtaining the keycard involves killing her while on your first date. Ken will call should that happen, CJ will explain what happened, and you'll have to break into her house in order to grab the keycard.