"This, Harry, is the charming village of Budleigh Babberton."
-- Albus Dumbledore (HBP4)
Budleigh Babberton is a small Muggle town with a war memorial in the center and a church. Horace Slughorn took up residence in a Muggle house there for a week while its owners were on holiday in the Canary Islands, and this is where Harry and Dumbledore visited him to convince him to return to teaching at Hogwarts (HBP4).
There is no Budleigh Babberton in the Muggle world. Its namesake, however, is most likely Budleigh Salterton – a coastal town southwest of Exeter. Also nearby are Chudleigh and Ottery St. Mary, two towns whose names Rowling similarly tweaked to create Chudley and Ottery St.Catchpole.