Okay I am giving up my favorite “secret” motel that I give to visitors….which is nearby but not “walking distance” from LAX. To be exact it is at the south end of Santa Monica on Main street (that borders on Venice) and is called the Seashore Motel:
http://www.seashoremotel.com/
They are family owned, kind of 60’s funky and super nice people. Plus you are smack in the middle of Main Street with tons of shopping and great restaurants around and 2 blocks from the beach. And there is a great little Italian owned espresso bakery place called Amelia’s which makes great breakfast and brunch stuff. So to me it is worth the short drive-which isn’t bad if you aren’t during the major rush hour times since you end up 2 blocks from places where folks are paying $400/night to stay in. You are only 3–4 blocks off of Lincoln and then just straight on to LAX again. They start at around $100/night but might cut you a deal if you are booking a number of dates.
Google has a good street view look at them if you type in their address and then choose street view:
2637 Main Street
Santa Monica, CA 90405
Oh, and they also have rooms with kitchens if that interests you.