Where to live between DTLA and PV?

My SO and I currently live in DTLA where she works. I just got a job in Playa Vista so we're looking to move somewhere between the two areas. We both go into the office 3x a week. I also attend USC part-time in the evenings so need to make that commute after work some weekdays.

We're looking to rent either a house or apartment - ideally 2+ BR and 2+ bath and 1200+ sqft. Budget is ~$6k/mo. What are some areas we should be looking at?

Appreciate the input!