A smooth dance, a ball sport, a place to stay, an Asian country, and a girl's name.
What's her name?
Juliet, all of the listed things describe a part of the NATO phonetic alphabet: Foxtrot, golf, hotel, India, and finally Juliet.
Why this works
This riddle cleverly uses the NATO phonetic alphabet, where each word corresponds to a letter. The "smooth dance" refers to the term "Foxtrot," the "ball sport" is "Golf," "a place to stay" is "Hotel," and the "Asian country" is "India." Finally, the answer is "Juliet," which is both a girl's name and the last word in the sequence, completing the pattern. The riddle plays on the idea of using these seemingly unrelated clues to lead to a unifying answer!