Smørrebrød can be bought many places, mostly for take-away. They range from simple to very fancy.
Link to a very famous smørrebrøds restaurant :
http://www.idadavidsen.dk/en-gb/cms/Welcome
The menu is only in Danish :
http://www.idadavidsen.dk/da-dk/catalog/Order-Form
More suggestions about restaurants serving smørrebrød from the visitcopenhagen page :
http://www.visitcopenhagen.com/copen...l-danish-lunch
Maybe this link about New Nordic Food is of interest to you as well :
http://www.visitcopenhagen.com/copen...ic-restaurants
And don't forget to visit some of our bakeries if you like cakes.