Lets admit it : Copenhagen is not a cheap place. VAT is 25%, Minimum wage is 120 DKK, making it one of the most expensive citys in Europe.
The general rule is: the longer from the city center, the cheaper it gets. That goes for food, clothes, accesories, cafes, bars. Off course there are some exceptions like places in Vesterbro and Nørrebro, but it works as a general rule.

Food
There are super markets everywhere in the city, and some are open 24 hours a day. My favorit is Irma, but they are also 20% above the prices of everybody else. The cheapest is Fakta, Netto, Aldi and Lidl, but they are also discount, selling shitty products.
Torvehallerne på Israels Plads, is a Mekka for food and drink lovers. You can spend a long time there, bying food, eating, drinking coffee, beer, wine, spirits. Good quality, and sometimes you can even find something cheap 😉

The cheapest food you find in the Turkish / Arab greengrocers around Nørrebro Station. For East Asian and Indian Food, head to Vesterbro, behind the central station.
Organic shops includes Natur og Sundhed on Nørrebrogade, Spidsroden in Griffenfeldtsgade have a lot of vegan organic food, helsemin Østerbro, on Østerbrogade by Trianglen. And then there are Lød Market on Saxogade by Istedgade on Vesterbro. Irma also have an All Organic Supermarket at Østerbrogade.

Wear

Most fashion is around Strøget in the center of the city. But it will be difficult to find something you cant find ín other bigger european Citys like all Main street retailers.
In Pilestræde and Grønne gade, there are some more local fashion.
For more independant shops you should head to ever trending Nørrebro and Vesterbro. In Nørrebro, go to Elmegade, Ravnsborggade, Blågårdagade and Jægersborggade. On Vesterbro go to Istedgade, Sønder Boulevard and some of the side streets here.

Design
Scandinavien design is the essence of scandi-collness. I think the best design store is Superlove, but also in Hay you find good stuff. For the more independent shops head towards Nørrebro, Vesterbro, Christiania. The Danish Design Museum and the National Museum has good shops. But you can even go to the local Flying Tiger, and find acceptable design.

Flea markets. (Loppe markeder).
There is one in Israls Plads every saturday. You find good stuff, but you also pay the price. Den Blå Hal (The Blue Hall) in Amager is a place to go, where you find stuff at reasonal prices. Open every weekend.
In Refshaleøen, the old B&W shipyard there is a fantastic huge market in all even weekends. This is where the traders have there store room, and it seems endless.
Local Street partys are mostly followed with a flea market. Private people sell out of there own things, and you can always find something. 90 % women clothes 10 % mens clothes and a lot of kids toys.
There are indoor Flea markets, and you pay an entry fee around 30 kr. Check my weekly blog.

Music
We are some people who still like to hold the good old Vinyl records in our hands, and feel the wheight of it. Best music stores are:
Route 66 (Vinyl only).
Sound Station.
Sort Kaffe og Vinyl (also a cafe).
Beat (also a cafe).
Accord (Second hand).
Insula Music (Mostly punk).
Jazz Cup. Mostly Jazz