If you are staying at a hotel in LA they can organise for one of the many bus companies running shopping trips to Mexico to come and take you for the day. It's a long day out for the return trip to Tijuana, Mexico.
Cost?
Varies but allow USD$40-$50 return
Why go?
Tijuana is a paradise for bargain shoppers! Browse for leather goods, clothing, jewellery, pottery & more.
Note - a multiple-entry visa and passport are required for non-U.S. or non-Canadian citizens.
Tijuana Mexico - south of the border
Updates
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If you have a rental car, just leave it at the last parking lot before the border and hop on the bus (10us$ for a return ticket).