Coffee shop noise is irrelevant, office noise might be relevant. You automatically pay attention even if you don't want to.
For me, noise cancelling headphones are a necessity. Impossible to get anything done otherwise.
What finally made me buy a good set of headphones for work was a cow-orker that would regularly come to my office to talk to a colleague about some project. Nothing to do with my work, but the words he used made me involuntarily tune in to the conversation every 10 seconds, just because it sounded relevant.
It's basically just ambient noises from a coffee shop, and you can choose a couple of different "environments". I pop that on in my headphones, and layer on some instrumental music. I love it.
Right now I'm in a cafe that has 50+ people and thumping bass music, all sweet white noise. With a beat.