WEST HOLLYWOOD. LA's original Farmers Market opened in 1934 when a handful of farmers gathered on a vacant street corner (known locally as Gilmore Island) to vend the season's crops. Today's market, easy to spot thanks to the famous clock tower that soars above it, has taken on a completely different persona and now offers more than 30 restaurants and an impressive array of specialty shops and open-air food stalls. The place is still steeped in history, but it's also a modern-day shopping and dining destination.