I understand that there is some debate between people from different countries as to whether one should wear outdoor shoes inside. I grew up in a shoes off household as did all of my friends in the UK. I personally find the idea of walking filth from the street into your house quite revolting especially if you have carpets. When I lived in Berlin my feet would be filthy after a walk in flip flops in our relatively clean neighbourhood so imagine how much dirt builds up on shoe soles!
So I had no problem when our first landlords in our Danish apartment stipulated shoes off whilst we lived there. It is the norm in Denmark for both residents and guests to remove their shoes at the door and either go in socked feet, your own slippers or borrowed ones from the host. I hear people, mainly from the US, complaining they are ashamed of their socks or feet. Easy answer – throw out old holey socks or do an at home pedicure. They also argue it feels too intimate but isn’t being invited into someone’s home an act of intimacy? Even tradespeople such as chimney sweeps take off their shoes or put on little plastic covers when entering a Danish home.
There were a few reasons our landlords gave, as perhaps they felt they needed to justify their demand, firstly they had spent a lot of time and money on their beautiful wooden floor and didn’t want scuffs or heel marks. Secondly the sound of shoes on the floor is disturbing to the neighbours below. Finally it is the cultural norm in a country where it is wet or snowy a lot of the year. Although they didn’t say so it’s about respect and also comfort.
I know people argue that as the floors are generally uncarpeted that they are easy to clean. Yes this is true but unless you run around behind people with a mop, there will be a build up of dirt. Danes entertain at home a lot but it’s more about the people, the food and the hygge than image so forget about showing off your Laboutins and get yourself a pair of hyggelig slippers – no one says they need to be boring!
You can buy monthly or yearly passes for the zones in the city or pay as you go using an app or one of the machines in the street. 
I thought I’d do a quick run down of what is available in the pharmacies (apotek in Danish) here.