I'm not sure whether "Santa Monica" and "affordable" can be used in the same sentence.
One exception would be the Santa Monica youth hostel, but that type of accommodation may not be to your liking. It does have some private rooms, but they seem to be frequently booked solid -- gee, I wonder why?
On the other hand, there are many decent hotels around LAX that are fairly affordable (lots of the standard chain hotels, for example). As others have pointed out, traffic (especially on freeways like the 405) can be very congested, so that has to be taken into account when figuring your driving times to/from the LAX area.