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Westfield Culver City is only a 10 minute Uber/Cab away. It has the usual mall shopping including Macy's, Victorias Secret, Ulta, Sephora, Nordstrom Rack (Nordstroms Outlet store), Bath and Bodyworks etc, etc along with a number of restaurants and fast food outlets . Stores at Westfield Culver City is also a Marshalls across the street. We grabbed an Uber to it one trip when we had a long layover and spent a few hours there. The closest actual Outlet Mall would be The Citadel Outlets which are a good 30 minute drive away, possibly longer depending on traffic conditions.
Westfield Culver City is probably the best bet, but I like going to Manhattan Beach Plaza. There is a $5 shuttle bus from Century Blvd that makes a couple of stops.
you can have a nice lunch in Manhattan Beach, go to the Aquarium and hop back on the shuttle to Manhattan Beach Plaza. You can also go to Plaza El Segundo which is just a couple of blocks from Manhattan Beach Plaza.
In the same area, Main Street El Segundo is a good place for restaurants.
Best Western Suites Plus is near LAX and across the road from a small group of shops - including a cheap looking Korean restaurant, a Pandas Chinese takeaway, liquor store and a 7/11. Apparently there is a Mexican place not far from there around the corner that others ate at. Scrambled eggs and bacon galore for breakfast in the hotel.
Not the most salubrious area (people sleeping in the shops' doorways at night), but the hotel's rooms are clean and spacious, and they have a shuttle. I picked the place because parking was US$12 a day, the cheapest I could find anywhere. So I really liked staying there, but my wife didn't because of the surrounds.
On my last trip through LAX I stayed at Courtyard by Marriott Los Angeles LAX/Hawthorne | Qantas Hotels - its only been open a short while but the management and staff are great, the rooms are really good and they have a free shuttle. There is a supermarket across the side street and takeaway stores there as well - its now my first choice for any stops in L.A.