Ahhh... street photography. It's all about finding beauty - or anti-beauty - in the mundane.
There are so many things beyond your control: the weather, lighting, who you're shooting and what that person is doing (unless you're doing a straight-on headshot) dealing with background clutter, shooting with minimal gear, etc.
Two ways: you can either be super stealthy for candid photos or barge in, guns blazing, with your usual "Can I take your photo?" spiel -- small talk and backstory included.
Oh, wait, Copenhagen. Bikes, concept stores, Scandinavian fashion and design, 'em photogenic Danes, more bikes, hipster havens (or hipsterhavns rather. Not one, but two hipster neighborhoods!), and *that* Michelin-starred resto [closed as of my last visit in July 2017] . Skip the Little Mermaid and lose yourself in Nørrebro and Vesterbro.
Where to Eat
Danish/Scandinavian: Restaurant Relæ + Hallernes Smørrebrød + Grød, Manfreds
Pizza: Neighbourhood Pizza
Copenhagen Street Food at Papirøen: Brasa (go for the chorizo!), La Fattoria's Porchetta Sandwich
Coffee: The Coffee Collective, Democratic Coffee
Where to Shop
Books: Cinnober (impressive Gestalten collection), ArnoldBusck.dk
Clothing & Concept Stores: Storm, Wood wood, Black, Legend, Street Machine, Han Kjøbenhavn, and all the cool stores along Jægersborggade (Sneakers & Coffee).
Music: 4sound (great synth collection), Accord (Audio CDs - yes, yes, at this day and age, still a resounding yes.)
Lego Store. Because you're in Denmark. Just for the heck of it.
Stuff for your house: Bolia.com, Illums Bolighus
Where to Shoot
Indre By (Gothersgade, before the shops open!)