Cheltenham became a town because pigeons landed in a Gloucestershire meadow in 1716 and people noticed the spring they were drinking from tasted of salts. By the time King George III visited in 1788 to take the waters for five weeks, the place was a national destination. The fortunes of the Regency boom built the town that survives today: cream-painted stucco terraces along the Promenade, ironwork balconies in Montpellier, the Pittville Pump Room rising above its park like a Greek temple in a kindergarten illustration. The town hall, opened in 1902, still bears its plaque commemorating the coronation of Edward VII. Nikolaus Pevsner judged Cheltenham Synagogue one of the best non-Anglican places of worship in Britain. Walking up the Promenade past the boutiques and the John Lewis store, the only obvious changes since 1830 are the cars.

On the western edge of Cheltenham, surrounded by ring-roads and very high fences, sits a circular building so unusual that everyone in town just calls it the doughnut. Government Communications Headquarters, or GCHQ, is Britain's signals-intelligence agency. About 6,000 people work inside, listening to the digital world. Cheltenham was chosen as the agency's home after the Second World War partly because it sat far enough from London to be defensible and partly because the Regency town's plentiful housing could absorb the staff. Today the doughnut anchors a quiet aerospace and electronics economy: GE-Aviation builds engine systems on the old Smiths Industries site, UCAS processes university applications from a vast office block, and the design houses Superdry and Weird Fish both grew up here. Cheltenham's unemployment rate was 2.7% in 2010 while the UK ran at 7.9%. The town is comfortable in a way that takes some doing.

Gustav Holst was born at 4 Pittville Terrace in 1874. His father was the organist at All Saints', Pittville, and the family lived above the music shop. By his late thirties Holst had written The Planets, the most-performed orchestral suite by a British composer in the twentieth century. The Holst Birthplace Museum on Clarence Road still holds his piano, his desk, a working Victorian kitchen and laundry, and a Regency drawing room arranged as it would have been when the Holsts moved out. Brian Jones, the founding member and original leader of the Rolling Stones, was also born in Cheltenham, in 1942. He learned to play guitar in a town that took its music seriously. After his death by drowning in 1969 he was buried at Cheltenham Cemetery, where Stones fans still leave flowers. The other notable Cheltonian musicians include Würzel of Motörhead and the singer FKA Twigs. The town hosts annual jazz, music, literature, and science festivals, and was named the UK's fifth most musical city by PRS for Music in 2010.

Pate's Grammar School, founded in 1574, is the oldest school in Cheltenham; Cheltenham College, founded in 1841, was the first of the great Victorian public schools, and its quadrangle stood in for the rebellious school in Lindsay Anderson's 1968 film if.... Cheltenham Ladies' College, founded in 1853, remains the most famous girls' school in Britain. The Cheltenham Cricket Festival, first staged at the College in 1872, is the oldest cricket festival in the world. None of this prepares you for the Wishing Fish Clock in the Regent Arcade, a 14-metre brass-and-bronze contraption designed by Kit Williams (of Masquerade fame), where mice climb a clock face and a fish gulps for wishes on the hour. Or for Banksy's 2014 graffiti of spies in trench coats next to a telephone box, a quiet joke about GCHQ that the homeowner removed two years later, probably for cash.

Cheltenham sits on the flat valley floor at the foot of the Cotswold escarpment, with Cleeve Hill rising abruptly to 330 metres to the north-east. The town's grid of Regency terraces and parks is unusually legible from the air; the racecourse is the green oval at Prestbury to the north, and the GCHQ doughnut is unmistakable on the western edge near Benhall. Gloucestershire Airport (EGBJ) lies just south-west, a busy GA field with Robinson helicopters and Cirrus singles in the circuit most days.