This historic strip in downtown San Jose has two of the city's oldest buildings—the Peralta Adobe and the Fallon House. The name is misleading because it's not really a square, but rather a one-block stretch of San Pedro Street. The area is a popular place for lunch, as most of the restaurants offer patio seating along wide sidewalks, and there is a multilevel parking lot on San Pedro Street. A farmers market takes over on Friday from 10 am to 2 pm. San Pedro Square is between Santa Clara and St. John streets, San Jose. http://www.sanpedrosquare.com.