Thank you all for the interesting and thoughtful responses. Each of you has given me some food for thought and I will eventually let you know what I have decided.
I thought that it would be so easy but ... famous last words.
I have thousands of miles with Southwest Airlines which does not fly to Europe but Southwest allows members to use miles to redeem for hotels, cars, insurance, gift cards, etc even when you are not flying them.
I had already checked and I was going to be able to get a Copenhagen Card using my Southwest Miles. Other options included Hop On Hop Off buses or entrances to places like Tivoli. I had been keeping my eye on the options offered all over the world through Southwest.
Friday, I decided that it was time to get serious. I went to My Rapid Rewards and clicked on "Experiences" and Copenhagen is no longer available as an option. There are only a very few cities available to redeem miles for "Experiences" and all of them are in The United States.
It could be maintenance or updating or a glitch. I can call but i have to wait until Monday.
I could book a hotel in Copenhagen using my miles but I have a great deal on a hotel already.
I may have to wait and use my miles to fly Southwest to Hawaii, Las Vegas, Disneyworld, The Caribbean, Mexico or book a cruise. Not bad.