Dr. Coriander Stripe, and ex-Mime scientist, is standing just inside the gate to the Pelican Bay boardwalk. He's quit the mime cult, but left his invisible props behind and needs them back in case he ever wants to mime again.
The missing equipment is being held by other mimes around the boardwalk, but some of them won't appear until after you've opened the Cataract during The Game Is Afoot. You can't return the items one at a time either; you'll need to have all three in order to get your reward.
Once you've given the briefcase, stairs and rope to Coriander, he'll give you some invisible weights in return; your character will use them immediately, increasing your attack stat by 10 points.