In Saints Row: The Third (aka Saints Row 3) for the PC, PS3, and Xbox 360, there are several strip clubs, but I have only found one that you can actually go into.
The name of the strip club is Technically Legal (lol) and you’ll find it in Ashwood, a block north east from the Nobody Loves Me clothing store.
Here is a view from the outside, it’s pretty hard to miss.
Once inside, there isn’t much to do really.. besides get down on the stripper poles of course! There is a mission that takes place here later in the game.