Almost every city has a local farmers market at least once a week, El Segundo's is every Thursday afternoon, from 3-7 pm and takes up the 400 block on Main Street in front of the Fire Department/Library/City Hall. There are stands that sell produce, prepared foods, and a few vendors who sell jewelry and clothes.
The biggest reason to shop at a farmers market is you are supporting the people who produce the products directly instead of a middle person who takes a cut for distribution. You may not find everything you may want here, but there are enough options to supplement your groceries from the big chains, and the quality is far superior while the prices are usually about equal. My favorite peaches came from the seasonal Summer stand who only comes when their fruit is in season.
Avocados are sold at several stands in varying sizes and varieties.
Mom's Products sells spicy olives, hummus, marinated artichoke hearts, and spanikopita (spinach and feta pastry), offering increasing discounts as you purchase more.
Gaytan Family Farm not only sells wonderful orange yolk eggs,
I loved the harissa from the Parmigiano-Reggiano spread stand; I always keep some on hand to spice up anything that needs some zing, whether it's scrambled eggs or fish.
The Chicken Guys sell parts or whole chickens for a great family take away option (there is also a Thai takeaway, tamale stand, pupusa stand, crepes, kettle corn, and swirling potato most weeks).
If you are in the area, it's worth stopping by, especially since parking nearby is easy and free, and they even offer a shuttle so that you may leave your car at home!