J.K. Rowling’s birthplace is listed as Yate, a town in South Gloucestershire, England.
She was born at Yate General Hospital on 31 July 1965. Yate lies northeast of Bristol, so biographies often describe her more broadly as being born near Bristol. That broader wording can make Bristol appear to be the answer, but Yate is the specific town associated with her birth.
Rowling’s family did not remain in Yate for her entire childhood. She grew up partly in Winterbourne and later in Tutshill, near Chepstow. Tutshill was especially important to her early life and is often connected with the inspiration and setting of some childhood memories reflected in her writing.
The nearby geography also explains why accounts may mention England, Gloucestershire, Bristol, or Yate at different levels of detail. Yate is the most specific answer for the town, while Bristol is the nearby major city.