"Sagebrush State" is Nevada's nickname, not a city. Among the locations mentioned, Las Vegas, Nevada is closest to San Diego at approximately 330 miles (530 km) by road—about a 5-hour drive.
Tucson, Arizona is roughly 380 miles (610 km) away. The Grand Canyon's South Rim is about 450 miles (725 km) from San Diego. Las Vegas's proximity and major airport make it a common weekend destination for San Diegans.
All three destinations offer dramatically different experiences: Las Vegas for entertainment, Tucson for Sonoran Desert ecology and culture, Grand Canyon for iconic geological scenery.