Agree with the 110! If you can drive the stretch of the 110 from Downtown to Pasadena everyday i'd be jealous. Of course that's assuming it's not rush hour. Rush hour is horrible as with virtually anywhere in LA unless you happen to be going against traffic. It's something you do get use to and live with. With that said, that's why I moved to Culver City even after living in Alhambra/Pasadena all my life.
There are certain areas in Culver City, West LA, Mar Vista, Westchester that fit your criteria. This would be west of Cedars. I probably wouldn't bother looking south into Crenshaw, nor into West Hollywood/Silverlake (unless you wanted to be with all the hippies). I wouldn't even bother looking in Koreatown or Miracle Mile (the roads are just horrible), but I would most certainly look further east like in Downtown (if you can live with the higher HOAs), then Monterey Park (if good asian food is important to you), then Alhambra, and then Pasadena. I probably wouldn't look any further into San Gabriel, Temple City, Arcadia, West Covina unless you were prepared for at least a 40+ min commute. AGain, this is all speaking in terms of rush hour. If your schedule allowed you to commute on off-hours then virtually everywhere in LA is 20-30 mins from Cedars. Oh, and I wouldn't bother looking into the valley (Studio City, Encino, North Hollywood, etc). Commuting thru one of the canyon artery roads (i.e. Laurel Canyon) that run thru the Hollywood hills SUCK during rush hour. However, I drive thru there often in the middle of the night and up Mulholland once in a while. The roads are fun at speed
Like I said earlier, Cedars is in a prime part of town. To stay within $1000/mon rent and have some semblance of a garage you need to expect at least a 30 mins commute.
I work in Brentwood but live in Culver City. It's only 7 miles and it still takes me 20 mins to drive to/from work.
If you find specific areas just post on here and we'll comment. Most of these towns have good and bad areas.