$2000 a month will get you a nice 1 bedroom or a 2 bedroom in older buildings in slightly less desirable areas (e.g. next to freeways). For 2 bedrooms in nice areas, the rent is more in the range of $2500~$3500.

Beverly Hills has very little apartment rental so you are looking at places like West LA (~$2500), Palms (~$2000), Culver City (~$2000), Rancho Park (~$3000 sometimes referred to as Century City in listings), Westwood (~$2500+) Santa Monica (~$3000+), Brentwood (~$3000+) - all to the west of Beverly Hills.

You may also want to see Marina Del Rey (~$2500) and Playa Vista (~$3000+) which are a little further down the coast but have lots more apartments.

http://www.westsiderentals.com/guest...1&searchType=g