LAX airport is centrally located in the SouthBay just 20 minutes north of Torrance, Palos Verdes and Manhattan Beach.  One affordable option from Chicago to LAX is Southwest Airlines. 

All major U.S. carriers fly into LAX, however depending on your point of origin you may be able to take advantage of discount airfare on airlines like Southwest or TED.  Southwest usually has tickets for around $120 each way if you purchase tickets very early.   Less expensive tickets are limited.

John Wayne or Orange County airport are located 45 minutes south of Palos Verdes/ Manhattan Beach.

The Long Beach Airport is also around 20 minutes from Palos Verdes/Torrance area.  They are a smaller airport with limited carriers.  However, Jet Blue is a very affordable option that does use their terminal.  Currently they have options for around $110.00 each way.  Tickets are limited. 

Keep in mind LA traffic can be a doosey.  Allow yourself plenty of time for any travel while in Calilfornia,

Renting a car is somewhat of a necessity to get around in the SouthBay area.  All major car rental companies service the airport.