Esta semana habéis bajado al centro.

English Translation

This week you went downtown.

Is “went downtown” really the best way to translate “bajado al centro”.
To me it seems more like: “went down to the (city) center”

As far as I know, downtown is very commonly used to talk about the city center, so both sentences seem to be pretty interchangeable.

Looking at a couple of dictionaries, the witktionnary seems to point towards downtown being the business part of a city, but oxford’s really describes it as the center.
And both give city center as a synonym

English Translation

This week you went downtown.

I agree that downtown is in fact a synonym for city center, however I think the verb bajar to me seems more like a physical “going down” as in down a hill. But if it’s phrased like this normally in spanish then it’s just my different way of phrasing it naturally.