We have a free afternoon and would love to spend it meandering in a cute neighborhood with shops, cafes, etc. that is more local-flavor than touristy. Any recommendations?
The really cute neighborhood is downtown at the marina where you can catch a canal cruise. However it is touristy.
I don't know about cute, but you could take the S-train Line C to Ballerup Station and follow Google Maps to Ballerup Church. This church is totally unremarkable ( = not touristy), but the pedestrian street leading up to it has several shops, cafes and restaurants. On the way back you can pass the station and visit the local mall. Then go directly from the mall to the station.