Something I love about Denmark is that there's a lot of room to be yourself. Because people here don't care about things like class, status, lifestyle choices and appearing a certain way. That's why I always find discussions on Mumsnet about being middle class (for instance) utterly bizarre. We just don't have those kind of discussions here - and to be honest, I don't think anybody knows what classes exist, and which one they belong to.
I also like how safe it is here. I'm not scared to go out at night by myself, because I know nothing will happen. When I'm home alone I feel good about leaving my doors unlocked...I know nobody is going to break in. I can leave my stuff at a table in restaurants and be sure that they are still there when I get back. Of course things aren't perfect here, but having that sense of security and safety means a lot.
Lastly, I really like our welfare system. Healthcare is free, university and education is free, nursery prices are on the reasonable side...and if you become unemployed, you don't have to worry about money, because most people are members of something called an A-kasse. An A-kasse is a sort of unemployment insurance company. If you become unemployed, the A-kasse will pay out 90% of your salary for 2-3 years, while you look for a new job. Of course on certain conditions (like you have to apply for two jobs weekly), but it's nice to not have to worry about having NO income while unemployed.
As for my favourite places in Denmark...obviously, Copenhagen is great. But I actually much prefer the area just north of Copenhagen, by the coast. I also really like Aarhus and the island of Samsø. Bornholm, as well. Skagen is lovely - it's the most northern town in Denmark, and the beaches there have crystal clear water. And wild seals that you can catch a glimpse of quite up close!
Unpopular opinion, but I also really like Faxe for their lime quarries.