Nordvest is a neighborhood in Copenhagen, which I guess very few tourists get to visit. While some tourists will probably head out to visit the colorful and multi ethnic Nørrebro, most people will return to the center instead if proceeding to Nordvest, which starts immediately after Nørrebro.
I admit that Nordvest isn't the most beautiful nor exciting place in Copenhagen. However, the area is definitely authentic so if you are looking for something REAL then you should go here.
There is nothing much to come for in terms of restaurants and cafes, but the area does have some sightseeing places such as the Grundtvig's church (Grundtvigskirken), The Churchyard of Bispebjerg and not least the nature resort Utterslev Mose, which is an amazing place.
Nordvest is honest, it's unpretentious and it's tough and rough. The area has had several social problems and problems with crime for many years, but personally I feel that things are starting to change and as it usually happens with these kinds of areas they suddenly start to become trendy. I think that this area could change into a new hip thing within the next years (and I'm sure some people would hate to see this happen, which I can understand).
Until then lean back and enjoy your ride among old factories, garages and bodegas. Don't pretend anything, just as Nordvest isn't pretending anything from you:-)