Despite her somewhat prissy, puritanical air, Priscilla has managed to stay in the Top 500 every year since records have been kept—it reached as high as Number 127 in 1940—appreciated for its delicacy and solid history.
A New Testament name, it was Priscilla with whom the apostle Paul stayed while spreading the gospel in Corinth. It was common in the ancient Roman world and later was a favorite of the seventeenth century Puritans, including Priscilla Mullins (Alden), remembered for her co-starring role in Longfellow's poem The Courtship of Miles Standish. There was also a sympathetic Priscilla in Hawthorne's The Blithedale Romance.
The most conspicuous contemporary bearer of the name is Priscilla Presley, and it's what J. R. R. Tolkien named his only daughter.
If you find the nickname Prissy too prissy, you could use the British-inflected Cilla.