Common offshore domiciles for hedge funds are the Cayman Islands and the British Virgin Islands; common onshore domiciles are Delaware, Ireland and Luxembourg. Each has a licensing category for professional-investor funds with lighter requirements than retail products, in exchange for restricting who may invest.
Allocators care about domicile because it sets the investor protections they can rely on: statutory segregation, mandatory audit, independent directors and the regulator's powers. Managers care because it sets cost, speed to launch and which investors they can accept.