However, one A-list couple have built their own home off the beaten track, in a small village between Lavenham and Stowmarket.
Game of Thrones star Kit Harington and co-star and Downton Abbey actor Rose Leslie purchased their 15th-century timber-framed thatched farmhouse – called Popples Farm – in late 2010.
The pair were apparently sold on the area by popstar Ed Sheeran, who has an estate near Framlingham and grew up in Suffolk.
Their home is in Brittenham, a village first recorded in the Domesday Book of 1086 and, as of the 2021 census, is home to just 321 people.
Almost the entire area is a conservation area, complete with ancient woodland such as Ram Wood and the emerging River Brett, and as a pretty village it is a popular spot for people hiking or cycling around Suffolk.
There is a 14th-century Grade I-listed church, called St Mary the Virgin, where people come for its unusual history.
The tower is built on the south side of the nave rather than at the west end, and its base serves as the main entrance porch, making it one of only 14 churches in Suffolk built with this distinctive architectural layout.
The nearest place to stop and get some essentials is Hicham Post Office and Stores, which is a five-minute drive or 50-minute walk away, really setting it up as a secluded spot for the celebrity couple to keep their two kids away from the public eye.
Their closest celebrity neighbors (that we know of) are supermodel Claudia Schiffer and her husband, film director Matthew Vaughn.
The couple made Suffolk their family home after falling in love with Coldham Hall, an Elizabethan Tudor manor near Bury St Edmunds, during a chance visit 24 years ago.