Aarhus is small enough that you can walk a first date across three neighborhoods in an evening, which is exactly what I recommend doing. The trick is picking the right starting block. Some parts of the city flatter conversation. Others flatter the view. A few do both if you know where to sit.
Latinerkvarteret for the classic walk-and-talk
The cobbled streets around Mejlgade, Graven and Volden are still the safest first-date bet in the city. You can start at Det Glade Vanvid for natural wine, drift down Klostergade for a second drink at Ris Ras Filliongongong, and end up eating something small at Langhoff & Juul without anyone feeling locked in. The streets are narrow enough that you naturally walk close together, and there are enough doorways to duck into if it starts raining, which it will.
If the conversation is going well, the area rewards you. If it isn't, you can be at the bus stop on Nørreport in four minutes and nobody loses face.
Frederiksbjerg for grown-up energy
Frederiksbjerg is where Aarhusianere move when they stop wanting to live on top of student bars. Bring a date here when you want the evening to feel like adulthood without feeling stiff. M.P. Bruuns Gade has the density: Pondus for a long dinner, Sct. Pauls Apotek for cocktails that are actually good, Cocoa for dessert if you've made it that far.
The neighborhood also has Frederiksbjerg Bibliotek and the small park behind it, which works as a Sunday afternoon move when you want to keep things in daylight. Coffee at La Cabra on Graven first, then walk up Frederiks Allé and see what happens.
The harbor for a date that wants to look like something
Aarhus Ø and the Dokk1 area photograph well, and that matters more than people admit on a first date. Walking out to the Salling Rooftop earlier in the day, then drifting north along the water past Iceberg and the harbor baths, gives you something to point at. In summer, the harbor pools at Havnebadet are an absurdly good third-date move, but for a first date the walk is enough.
End at Nordisk Spisehus or, if you want it more casual, at Restaurant Domestic's bar seats. The water means you always have a reason to pause and look at something other than each other, which is a gift early on.
Trøjborg when you want to skip the performance
Trøjborg is the one I send people to when they're tired of being seen. It's a ten-minute walk north of the city center, mostly residential, with just enough cafes and small restaurants on Tordenskjoldsgade to fill an evening. Café Smagløs for an unfussy start, Sidesporet for beer, and the walk back through Risskov forest if the weather cooperates.
Nobody is dressed up here. The lighting is bad in a charming way. If you both like it, you've learned something useful about each other.
A note on Vesterbro and the student belt
I'd avoid Jægergårdsgade for a true first date, even though I love it. It's too good. You'll spend the night running into people one of you knows, and a first date needs a little anonymity to breathe. Save it for date three, when running into a friend becomes a feature instead of a bug.
Whatever you pick, build in a transition. Aarhus rewards the second venue. The first place is where you settle your nerves. The second is where the actual date happens.