I am not familiar with the area that is walking distance from the LAX Marriott.
But, with a week of evenings (and possibly a weekend or some whole days) to kill, I would definitely make my way to the area around the Hermosa Beach Peir where there is an amazing beach, interesting if touristy pedestrian walkway/mall along with an amazing walking/biking path along the beach. Venice Beach is another area with great people watching, cafes and general outside street life. Traveling to/from either from the LAX area via bus will kill around an hour; I am not sure about taxi fare but would guess under $30 each way.
The other thing I would consider is renting a car for a day and driving north up the PCH/Hwy1 for a while and maybe stop at some of the parks around Malibu.
If there's one thing in my life that's missing; It's the time I spend alone
Sailing on the cool and bright clear waters; There's lots of those friendly people
Showin me ways to go; And I never want to lose your inspiration