I've heard that Iceland is a pretty good destination. Greenland however is even more arctic and not quite as hospitable, unless you are attuned to what's there (as with most places).
Except for the prices, I'd like to visit some of the grand old hotels in the U.S., the Grand Hotel on Mackinac Island for a few nights, or Hotel Coronado on Coronado Island off San Diego. My wife and I had breakfast at the Carlyle in New York City and it was pretty fine, expensive but worth the visit.
My late wife and I went to the Jefferson Hotel in Richmond, Va., for an overnight and had Sunday brunch just off its vast lobby atrium with a fountain and potted trees, a place with a lot of history and atmosphere.
The Grove Park Inn in Asheville in the mountains is memorable, where F. Scott Fitzgerald and Zelda were guests -- mostly Scott while she was hospitalized for her mental troubles.
It was fun staying in the New York Arts Club at Gramercy Park in NYC, not a snazzy hotel, but an interesting place to spend the night, like sleeping in a museum.