I put my parents up several times per year in the area and have usually been able to find decent sales at one of the Pacifica Group Hotels around the Marina (i.e. sub $200 rates). But it looks like in August they are much higher even with a current 20% off sale - seems to be the same for most of the other hotels I have found deals at in the past (i.e Hampton Inn Santa Monica, Ambrose, Culver Hotel, 4 Points Culver City). I searched in the area for a few dates in August and seems the most affordable options are the Travelodge Culver City as mentioned along with the nearby Ramada Culver City and then the Best Western Royal Palace Inn & Suites which is a couple minutes further north/closer to UCLA up Sepulveda. The Holiday Inn Express is also sub $200 but barely - also the reviews say it has noise issues.

The Ramada seems to have ok reviews, but it is located right next to two other motels that are a bit lower on the food chain - I would probably avoid that specific row of lodging.

The Travelodge is close to the Ramada but has separation from the other area so should be fine. I actually lived around the corner from it for 14 months and the area is safe enough, though you may hear an occasional police helicopter fly overhead which is par for the course in parts of LA. The Travelodge also has a nice little diner in it called the Metro Cafe and several food options within a couple blocks.

Best Western is a little closer to UCLA but generally you can get into Westwood from the south without too much of an issue - so I would consider all these hotels ok for driving to UCLA.

If you are really on a budget but want to get a class above these options, I would consider studying the LA hotel lists on one of the bid tracking sites for the Brentwood - Westwood and Culver City zones, and maybe even Venice-Santa Monica and LAX zones as well, and priceline something for two nights. I think there is a decent chance you get a 3* or even 4* near the airport in the low 100s and perhaps in Westwood proper for $200ish.