The LA West Travelodge has been where I've hung my hat for about a year of business commuting, with monthly stays of about 4 nights per visit. I chose it because it's not the LAX Motel 6, it's near bus lines on Westwood and Santa Monica Blvds, and it's pretty much the cheapest rate you can find in LA.
The downsides: The property is badly in need of refurbishing, and nearby Santa Monica Blvd is basically a raceway. My advice: ask for a second-floor room when you arrive. The rooms get very warm and usually don't have enough windows, so you'll be running the air conditioner most days out of the year. You can generally leave the AC on during the day while you're out, without the maid turning it off, if you leave the temperature set to "normal." That helps keep it cooler. Depending on how loud the AC turns on and off, which varies depending on the room, I've generally found I get a restful night's sleep only when wearing earplugs, but I'm a fairly light sleeper. The shower heads are pretty searing and positioned too low. They do indeed have a pool, but it's never available when I'm there, before or after business hours. They lock it up, for obvious reasons.
The upsides: Although it won't look it when you arrive, the surrounding neighborhood, near the Mormon Temple, is actually pretty decent. I jog during the mornings southward down Overland Ave, past an elementary school. There's a Seven Eleven right across the street. Each room I've stayed in also has a mini refrigerator. Santa Monica Big Blue Buses troll along Westwood and Santa Monica up to Westwood, but that's about a 4 block hike. It's incredibly cheap for LA, which is no doubt why the place is in disrepair. You get free bagels/danishes/coffee in the mornings until 10am. The service tends to be pretty good, although the morning guy is a little odd. And best of all, they frequently have rooms available, and you can cancel up until 4pm day-of. They claim not to guarantee parking, but I've never had a problem with it. You probably will want a rental car in this location, since it's far from anything including Westwood, unless you enjoy waiting for buses. (I kind of do!)
Bottom Line: Cheap! You'll save money, but you won't want to hang out there a whole lot.
This review is the subjective opinion of a TripAdvisor member and not of TripAdvisor LLC.