If staying in West LA , you'll want to skip the concrete paradise and head off to that of the beach variety, namely to Santa Monica. An alternative and cost effiicent way to get there is to take an MTA bus, especially on Santa Monica Blvd. Route 4 or 304 ends just steps away from the shore, on Ocean Ave. Taking a bus cuts the price and headache of parking in the popular Santa Monica. Wait times for these two buses are usually less than 10 min for either for most of the day. If taking the 304, there will be less stops, so this is the slightly faster route.
Along the Westside portion of routes of the 4/304 are the Century City mall and off-Rodeo shopping in Beverly Hills (by Beverly Dr. /Santa Monica Blvd), besides the beach.
If you find yourself without the car, the Metro Rapid bus 720 can get you around to some key points of West LA interest. The line runs along Wilshire, from as far west as Santa Monica and enters several different neighborhoods, including Beverly Hills, Westwood, and the small but elegant westside community of Brentwood. Warning: this is the busiest Metro bus by far. Try to not ride this bus during the peak hours of 3PM-5PM any day of the week.
If you are without the wheels, using the Culver City Bus #3 is very helpful for your West L.A trip. Instead of doing a grid-like travel on the street, the route crosses through major points of interests in the area, such as the Fox Hills Mall and Century City mall (or Westfield malls). By crossing the routes, some traffic time is cut. Any shortage of traffic in the LA area is desired.