I have lived in Denmark all my life.
Education is known to be pretty decent, so it's not a bad choice to want to study there. However, I have no knowledge of the pricing for foreigners and the availability of classes/education being conducted solely in English.
Copenhagen is most likely the place most go to study, and therefore there is in general a lack of student housing. But it is a very expensive place to live, and tax rates ranges from approx. 32-58% depending on your income and town of residence. In turn, at least for Danes who pay tax legally, hospital and doctors fees, not to mention education, are all covered by the taxes everyone paid for.
Young people in Denmark loves to go out, party and drink, so you should be prepared for a big drinking culture. Food in general is expensive in Denmark, and since we have strict rules for food sold in stores, it goes bad quickly compared to other countries whose food is filled with preservatives.
Denmark is known to be a safe place, and also has one of the highest rates in solving crimes.
Denmark, or Danes, has a bad reputation for being racist internationally, part of it being that Denmark has a very strict immigration policy, because Denmark has some problems with immigration that they can't seem to solve.
If you live in the capital, one of the most common ways of transport is by bicycle, and it's relatively easy to get around that way.
Denmark consists mostly of islands, and the country has a long history of wars (i.e. Sweden and Denmark has the biggest number of recorded wars in the world between the two countries)
Because of the sea-climate, both winters and summers are very mild. Winters are relatively warm, and summers relatively cool. Be prepared for a cloud-covered sky and rain.
Anything else you'd like to know?
Btw the statue "The Little Mermaid" is actually as big as the name implies: "little". Most tourists are surprised to see a statue that is far from huge.