They can be found in and around their ship, the Marie Elena docked at the Imperial City Waterfront. They will attack if someone gets too close to their ship. Killing them when they attack is not considered murder, so local Imperial Guards will come and help. The pirates in the Waterfront are led by Captain Gaston Tussaud and First Mate Malvulis.
With the Thieves Den plugin the Hero of Kvatch can have their own pirates, at Dunbarrow Cove, that will sail out and plunder once a week. The old pirates must be defeated, and the Black Flag must be claimed first.