Neighborhood recs -- moving from DC with 7 month old, working DTLA 2x a week
I (mid-30s) am moving with my husband and 7 month old to LA and looking for neighborhood recommendations. I will be working in DTLA two times a week and my husband works from home. We are looking for a 3 bedroom place with a budget of $6000. I would be grateful for recommendations of neighborhoods where it's nice to do stroller walks, has parks, and has a few things we can walk to, like a cafe or grocery store. We are also okay with being in a less lively / more suburban neighborhood as long as we are within a 5-10 minute drive from a commercial street.
We previously lived on Capitol Hill in Hill East and there was a lot of crime in our specific pocket (4 shootings on my street in one year) and we would like to avoid this. So far I am considering Pasadena, NoHo/Valley Village/Studio City area, and Culver City, since the commutes don't seem horrible and there is public transit (I have a car but would prefer to have the option of taking the metro to work). All recommendations welcome!