If a person could visit no more than one country outside the United States, what would be most recommended? (It doesn't have to be a "country.")
That really all depends on the person OP.
One person may love Italy, another may hate it, but instead love India. Someone else may be more fond of New Zealand or Japan.
There is no one answer.
Why do you ask about a country, OP, then write that it doesn't have to be a country? What does that mean?
If you're traveling to another country for the first time...good for you! Travel gives us a better insight into our lives and helps round us out as a person. It is a sad fact that all too many Americans never travel and when they do, they aren't interested in learning about other cultures but instead spend all of their time finding reasons to shout "USA the best" in their teeny heads while doling out Euros in MacDonalds donned in sweats and bulging out of their stained tee-shirts.
Live, learn, develop.
Egland and Spain are two of my favorites. I enjoyed France, but only stayed in Paris. Would probably have enjoyed it more if I had been able to travel to some other regions.
Traveling allows you to develop pretentious utterances and to broadly stereotype the residents of your home country as if you no longer live there.
Go for it!