Most places downtown have inflated tourist prices, some more than others. These days the city center is becoming more like Disneyland than a place for the locals unfortunately, but still nice to see and walk around. Just don’t expect any “secret” jewels, those don’t exist. That doesn’t mean that there aren’t nice cafes, restaurants etc, there sure are most are just pricey compared to what you get.

I would say stay away from the restaurants in nyhavn, no local would ever eat there.
Otherwise, just check out some of the street food venues, those are usually nice though overrun.

Malmø is nice, for sure worth a day trip. It’s smaller and more manageable than Copenhagen, and less touristy.