Marinas packed with mega-yachts. Glossy restaurants with Instagram-famous DJs. Glitzy beach clubs with bottle-service cabanas. For many visitors, Sardinia begins and ends with Costa Smeralda, the glittery playground on the island’s northeastern edge that has long defined its image abroad. Developed in the 1960s by the Aga Khan IV, the billionaire Ismaili spiritual leader, the area remains synonymous with Mediterranean luxury. But when I drove south, that version of Sardinia began to fall away.