There's the Copenhagen on the postcards and there's the Copenhagen people actually live in, and the dating happens in the second one. The first one has Nyhavn, the harbor canal tour, and dinner at a place with a Michelin star and a six-week wait. The second has natural wine in a back room in Nørrebro and a swim at a dock you've never heard of. Here's where the locals I know actually take each other.
Værnedamsvej, all of it
The little street between Vesterbro and Frederiksberg that locals call "the French street" is a date neighborhood unto itself. Falernum is the natural wine spot, Bibendum is the more grown-up version, Granola is the all-day cafe with the best people-watching, and Juno the Bakery is two streets over for the morning-after move. You can spend an entire date on one street and not get bored, which is the whole point. The crowd is local, the prices are reasonable for what you get, and nobody is taking photos for Instagram.
A proper Værnedamsvej date goes: drinks at Falernum, walk the street, dinner at Lecoq or Frederiks Have, nightcap somewhere on Vesterbrogade. That's a Saturday.
Assistens Cemetery in summer
If you tell a non-local you're going on a picnic date in a cemetery they'll think you're being a goth. Assistens in Nørrebro is not that. It's a public park that happens to also be a working cemetery, and on a sunny Saturday in June it's full of couples on blankets, friends drinking rosé between the graves, and parents with toddlers. Hans Christian Andersen and Kierkegaard are both buried there, but mostly nobody cares. Bring wine, bread from Mirabelle a few blocks away, cheese from Unika at Torvehallerne. It's the most relaxed date format the city has, and it costs nothing.
Sandkaj and Sluseholmen swimming docks
Tourists swim at Islands Brygge because that's the one in the guidebooks. Locals swim at Sandkaj in Nordhavn or at Sluseholmen in the south. Both are designed for swimming, both are clean, and both are free. Sandkaj has the better cafes nearby (Gorilla, Aamanns 1921 around the corner) and the after-swim crowd is younger and more date-oriented. A swim, a beer at the dock, a walk through the new Nordhavn district. You'll see Copenhageners doing the exact same thing.
Neighborhood wine bars
Copenhagen has a deep bench of small wine bars that locals rotate through. Pompette on Møllegade in Nørrebro, Ved Stranden 10 in the city center, Den Vandrette on the canal in Christianshavn, Vinhanen in Vesterbro. None of them are flashy, all of them have a small menu of plates that work as dinner, and all of them are loud enough that the conversation has cover but quiet enough that you can hear each other. This is the standard local Tuesday-night date format. Two glasses, three plates, an hour and a half, home by ten.
Den Vandrette is the most romantic of the four, because of the canal-side seating in summer. Pompette is the one you go to with someone you already know. Ved Stranden 10 is for a first date because it's central and you can leave easily.
Reffen and Refshaleøen on a Sunday
Reffen, the street food market on Refshaleøen, gets dismissed sometimes as touristy, but locals do go, especially on a Sunday afternoon in summer. The trick is to go for the walk and the harbor bus ride more than the food. Take the 991 or 992 from Nyhavn, eat something, walk along the water to La Banchina for a wine, and bus back. The whole afternoon costs maybe 250 kroner per person, and the boat ride is the date.
Sankt Hans Torv on a weeknight
The square at Sankt Hans Torv in Nørrebro is the local equivalent of a town square. There's a cafe (Pony), a bar (Kalaset), and a coffee shop (Props), and on a warm weeknight people sit on the benches with beers from the kiosk and just talk. It's not a destination, it's a hangout, which is exactly why it works. If your date is going well at one of the cafes, you can spill out onto the square. If it's not, the metro is two minutes away.
A word on Noma and the fancy version
Noma exists, and it's worth what it costs if you can swing it, but no Copenhagener is taking a date there. The local equivalent of a special-occasion dinner is somewhere like Pony, Bæst, Marv & Ben, or Hyttefadet. All of them are bookable a week ahead, all of them clock in around 600 to 900 kroner per person, and all of them are restaurants people actually celebrate at. Save Noma for when your parents visit.