I think the biggest obstacle was for my wife to connect with other Danish women. Basically how to find friends, since social norms and culture is different.
That lasted 6 months, and she now has a big group of friends consisting of expats/danes.
Job opportunities are very good, especially if you work within healthcare, engineering or similar fields. There's a shortage in the workforce for highly qualified workers.
Pretty good. Lot's of opportunity for an American. Cost of living and taxes are very high, but then there is of course public healthcare, schools and education paid by taxes.
I can only speak for myself having lived in Copenhagen/Boston/NYC; cost of living is lower in Copenhagen, but so are salaries, expect a huge cut in pay as well as on your ability to live a comfortable life on a tech salary.
In NYC I can do a normal sit down lunch at $40 multiple times a week, without really batting an eye - whereas that would be painful in Denmark - on the plus side you usually have catered lunch which quality, choice and taste wise is not nearly as good, but significantly cheaper and with it being better for team work within the company.
For health care you should expect longer lines and significant delays in case you have a non-urgent issue; whereas that in NYC is something you can handle easily by setting up an appointment on Zocdoc so that you can see a specialist the next day - with it being covered by your health insurance.
On a NYC tech salary I tend to buy gadgets / items as often as I want, if the cost is below maybe $200, in Denmark that threshold is more like $60.
Vacation policies are generally substantially better in Denmark; and workload also being significantly lower.
Healthcare in Denmark is just fine in my opinion. We also hold a private insurance through work.
What is it you feel you need to wait for?
Also, in regards to salary: Yes, it's lower overall. But it's still high, especially in the tech sector. I get paid roughly the same as my US counterparts (we have offices in Copenhagen and New York).
It's tough for me to say - I've generally been doing 40-70 hours a week in NYC, and average in Copenhagen is more like 35 (defacto); In NYC I'm expected - more or less - to be available 24/7 incase of outage / stability issues, wrt my company, whereas it in Denmark is more about the client/company adjusting to your work schedule, and them living with potential outages.