There are a huge number of bookshops in Copenhagen so the following list is very much my personal choice but at least this illustrates a few of the options.
Arnold Busck is a good modern bookshop with a good selection of books on design and architecture and a wide choice of maps and travel books so useful if you are travelling on to other places after Copenhagen. It does have a coffee shop if you get entrenched in your browsing. One odd advantage/disadvantage of Busck’s is that the large art books are on an upper level and reached by pretty steep circular staircases - one at each end of the shop. Curiously this stops me buying too many large coffee-table books because I keep seeing images of the Rowlandson print with visitors to the Royal Academy tumbling down a spiral staircase and wonder how odd my obituary might be if I fell here and died under a huge pile of architecture books I was carrying to the till.
Arnold Busck is on Købmagergade, just south of the huge round tower of Trinitatis Church - the parish church for students at the University. The tower, built in the 1630s, looks like a water tower but appropriately housed the university library at one stage and there was an observatory on the top.
Paludan’s at Fiolstræde 10-12 is actually in the middle of the university - or at least the city-centre part of the university. It has a large comfortable cafe with tables on the street which is a fantastic place to sit and read what you have just bought or a place to sit and people watch while you wait to meet up with friends - although I’m not sure the owner’s would be too happy to have such a review - oblivious to the commercial problems in trying to keep a good book shop viable.
Further west is the Atheneum Academic Bookshop at Nørregade 6, on the corner immediately south of Vor Frue Kirke - the cathedral church of Copenhagen. There is a good range of books here and, as the name implies, this shop is at the serious end of browsing.
There are scores of antiquarian and second-hand bookshops in Copenhagen. Peter Grosell Antikvariat at Læderstræde 15 has a good selection of high-quality prints and further east on the same street is Bøger & Kuriosa at Læderstræde 9 which has an extensive selection of second-hand books on architecture and design along with copies of design journals and magazines - a really good selection - but I had to include them in this list anyway because of their name plate. It must rate as one of the oddest shop signs in Copenhagen.