As one that lives in the area, I can tell you that the closest, reliable park with the easiest access to Beverly Hills is Valencia Travel Village. Stay completely away from Florence/ Bell for lots of reasons. They ALL have traffic issues getting to BH in the morning, but Long Beach and Malibu will completely suck. Long Beach is simply too far and can easily take twice the time, and if ANYTHING goes wrong on the coast, there are few alternatives. Nor is it conveniently located. It's just a nice place to hang.
There is one other slightly closer in the Van Nuys area that I know little about except its on the west arrival and departure of helicopter traffic to VNY.
Valencia to BH has the 405' and several canyon roads that drop into the area. By far the easiest access of the bunch. I take that freeway from Valencia past Beverly Hills exits daily and know the patterns all too well