Marin C.
Yelp
Rick Steves recommends this place, so there's that.
My mother and I had a room that was off of the main road, but we did still hear some clattering over cobblestones super early in the morning. Our friends who had a room on Nyhavn, well it was graduation weekend so people were partying all night.
Now, very comfortable rooms. Modern, you put your key card in to turn on the lights so you cannot waste electricity when you aren't there. Comfortable size and linens. Good service and tasty continental breakfast. Helpful in telling/ calling or assisting w/ calling taxi's for the airport (though they do have uber here).
Location, location, location. Walking distance to shopping to your hearts content, restaurants, boat tour etc etc. You'd need to cab or bike to see lil' ms. mermaid though, that's another review, eh.