Moving from USA to Madrid

Hello Everyone!
My family (wife and 3yr old) will be making a giant leap from Los Angeles to Madrid in about 4 months!
I was hoping to get a few tips regarding areas to live between Madrid (centro) and Fuenlabrada.
Work will be in Fuenlabrada but we want to be near the city as we will be going there as often as possible to not miss our culture so much. Korean descendants but practically lived in USA our whole lives.
Please let me know where i should be looking for housing! Alcorcon? Getafe? Leganes? Or just stay in Salamanca and commute? I hear traffic is not so bad (LA IS THE WORST)

We are looking for safe neighborhoods (and from what ive been seeing on idealista lots of places further north have great apartment ammenities.

Thanks in advance!

Salamanca is full of people your parents age and boring international brands. If you have a 3 years old, go to Plaza de Olavide and your kid wouldn't want to go home. It's full of young families with kids that age play together and the residential area around it, Trafalgar Chamberi is my favorite in Madrid. It's traditional residential and calm, and yet you can walk to Gran Via in 15 minutes.  What is a good area is very personal though, you should come and stay in a temporary place for a month or so, take your time and find the place that suits you and your family the best.

How about Pozuelo de Alarcon or La Moraleja?
We live in La Moraleja because it's very international due to the many international schools there. Not cheap though...