The historic Hancock Park neighborhood is a good running option in central Los Angeles. This residential enclave, located just east of La Brea, has very pretty streets, with lovely trees, attractive homes dating back to the 1920s, and period lamps. We actually prefer running in this neighborhood compared to Beverly Hills, because many of the posh homes in Beverly Hills are hidden by hedges and landscaping.
You can do several miles in this neighborhood by looping up and down the lengthy, flat streets. It’s ~2 miles east-west from S Western Ave. to South La Brea Ave. and ~1 mile north south from Melrose Ave. to Wilshire Blvd. Note that the posh Wilshire Country Club sits in the middle of the neighborhood.