Picking the right neighborhood matters more than picking the right bar. The wrong postcode means a tense walk from the metro and a venue you both feel obligated to like. The right one means options if the first place is loud, and a graceful exit if the chemistry isn't there. Here's how I think about Copenhagen by district when I'm planning a first date.
Vesterbro for low-stakes drinks
Vesterbro is the safest bet in the city for a first date, especially if you're both arriving from work. The Meatpacking District (Kødbyen) has Mikkeller's flagship taproom on Viktoriagade and Warpigs a few doors down, and if those feel too beer-bro you can walk five minutes to Lidkoeb on Vesterbrogade for cocktails in a converted pharmacy courtyard. The genius of the area is density. If your first spot is too crowded, there are ten more within a three-minute walk. Værnedamsvej, the little street locals call the French Quarter, is the move if you want wine bars instead. Falernum and Bibendum both work, and you can drift between them without committing to a full evening at either.
Vesterbro also gives you graceful escape routes. If things are going well, walk east toward the lakes. If they're not, Hovedbanegården is right there.
Nørrebro for talkers
Nørrebro is where I send people who actually want to have a conversation. The Jægersborggade strip has Manfreds for natural wine and small plates, Coffee Collective two doors down if you're doing a daytime date, and Mirabelle's bakery if you want pastries to walk with. The street is short enough that you can do a slow loop and not feel like you're trekking.
If Jægersborggade feels too on-the-nose, walk over to Sankt Hans Torv. Pony, Kalaset, and Props Coffee Shop all sit within a block of the square, and the square itself is a fine place to sit on a bench with a beer from the kiosk if the weather cooperates. Assistens Cemetery, where Hans Christian Andersen and Kierkegaard are buried, is a five-minute walk and surprisingly romantic in summer. People picnic between the graves. It's less morbid than it sounds.
Christianshavn for the slow walk
Christianshavn is for the date where you already know you like each other and want to draw it out. Start at Café Wilder or Sofiekælderen on the canal, then walk along Wilders Plads. The houseboats, the bridges, the smell of tar and water. It does the work for you. If you want food, Barr on Strandgade does great Nordic-leaning bistro plates without the Noma price tag (Noma is in the same neighborhood, but that's a third-date conversation).
Skip Papirøen unless you specifically want street food and crowds. Reffen, further out on Refshaleøen, is better in summer, and you can take the harbor bus there, which is its own kind of date activity.
Indre By for the classic version
If you want the postcard date, walk Strøget at golden hour, end up at Nyhavn for one drink (one, not two, the prices are punishing), then duck inland to Apollo Bar at Charlottenborg or Ved Stranden 10 for wine. The old town is touristy, but it's touristy because it works. The trick is to use it as scenery, not as your destination. Eat somewhere on a side street like Læderstræde or Magstræde instead of the main drag.
Refshaleøen for the unusual one
If your date told you they're tired of the same five wine bars, take the 991 or 992 harbor bus to Refshaleøen. La Banchina is a tiny wine bar and sauna on the water where people swim between glasses, even in winter. Lille Bakery a few minutes' walk inland does sourdough and natural wine in a converted industrial space. The whole peninsula feels like a different city, and the boat ride out gives you something to talk about before you even arrive.
A note on logistics
Copenhagen is small enough that you can change neighborhoods mid-date. A drink in Vesterbro and dinner in Nørrebro is fifteen minutes by bike or bus. Use that. The best first dates I've been on here moved at least once, because the act of walking somewhere together is when the actual conversation starts.