Portugal’s Algarve region is known for its stunning beaches punctuated by sandstone cliffs, and adorable towns, where cobblestone streets wind between brightly tiled buildings and town squares are lined with charming terrace restaurants. Here are our picks for the most romantic hotels in Porches, Albufeira, Lagos, Vilamoura, Faro, Sagres, and Tavira, in southern Portugal's beloved Algarve.