Did you know that Copenhagen has a one of a kind city layout? In fact, Copenhagen was the first city in the world to use this special layout, the fingerplan. Yes, there is an actual city plan called the finger plan, you can wiki it here https://en.wikipedia.org/wiki/Finger_Plan.
Many major cities use some variant of a grid layout, from which the city eventually grows. The advantage of the finger plan is that rather than to grow around a square grid Copenhagen has grown from 5 “highways” which is supported by public transport. This means that transport is much faster and straight forward from the city center to the suburbs.
This also makes it easier to determine where to find cheap housing. The further out the “fingers” the cheaper rent and housing becomes. Keep this in mind as a rule of thumb.
Normally in a capitol you want to stay as close to the city center as possible, transportation to and from work, school and events take a long time. But in Copenhagen the “core” is smaller since a larger part of the residential areas are placed along the fingers. Getting to and from the suburbs is fast and convenient, you don’t need to live in the middle of everything since it’s so easy and fast to get there.
The images below are from google maps, it shows the “fingers”. The yellow are the roads while the green lines are the train tracks. If you an on a tight budget a real possible is to look further away from the city center than you would at first. This is an option many Danes use ourselves, many people live in the suburbs in order to save on rent and cheaper home prices.