Cambridge

Everything radiates from King's Parade, the street that runs past the chapel's long flank. Climb the 123 steps of the tower at Great St Mary's, the University Church, for the one panoramic view of the spires. A few paces away, at the corner of Bene't Street, crowds gather around The Corpus Clock: a gilded dial with no hands, topped by a grasshopper-like creature called the Chronophage, the "time eater", which appears to devour each second as it passes. It was conceived and paid for by alumnus John Taylor and unveiled by Stephen Hawking in 2008. Round the corner is The Eagle, a coaching inn open since 1667, where on 28 February 1953 Francis Crick walked in at lunchtime and told the room he and James Watson had "discovered the secret of life". Look up in the back bar: Allied airmen burned their squadron numbers into the ceiling with candles and lipstick during the war. The audio guide here tells both stories.

North along Trinity Street the colleges grow grander. Trinity College, Newton's college, keeps its treasures in the Wren Library, where A. A. Milne's original manuscript of Winnie-the-Pooh sits among the cases. Next door, St John's College was founded in 1511 by Lady Margaret Beaufort, mother of Henry VII, and its nineteenth-century Bridge of Sighs, a covered stone crossing modelled on the Venetian original, is the most photographed bridge on the river. You cannot walk across it, but the view from the river or the neighbouring Kitchen Bridge is the one everyone wants.

The signature Cambridge experience is a punt: a flat-bottomed boat pushed along with a pole, drifting under eight bridges past the backs of seven colleges. The Backs are the strip of green between the river and the college walls, and from the water you see the colleges the way they were meant to be seen. Scudamore's has run punts here since 1910; you can hire your own, but a guided trip or an audio guide playing from your pocket turns the drift into a narrative. Watch for the timber Mathematical Bridge at Queens' College, rebuilt in 1902 and wrapped in myths about Newton and missing bolts, and for the gardens of Clare College, among the oldest and loveliest on the river.

Cambridge's museums are free, numerous and mostly walkable from one another. The Fitzwilliam Museum, a neoclassical palace on Trumpington Street, is strongest in Egyptology and Roman sculpture but ranges across Old Masters and armour. Across Magdalene Bridge, Kettle's Yard is something else entirely: a row of converted cottages that was the home of Tate curator Jim Ede and his wife Helen, kept exactly as they lived in it, with Brancusi and Ben Nicholson arranged among pebbles and houseplants. Smaller university collections round it out, from the Sedgwick's 4.5-billion-year walk through earth history to The Polar Museum and its Scott expedition relics.

The town is older than the university. The Romans built a fort called Duroliponte on Castle Hill around AD 70, and William the Conqueror raised a castle there in 1068; the grassy Castle Mound that survives is the best free viewpoint in town. Follow the river upstream through Grantchester Meadows to the village the Cam flows from, a two-mile walk that students have been making for centuries. On Parker's Piece, the open green east of the centre, the first rules of association football were played out. With more time, take the short train to Ely Cathedral, whose octagon lantern tower rises over the flat fens like a ship.

Direct trains run from London, Norwich, Brighton and Birmingham, and the station is a twenty-minute walk or a quick bus ride from the centre. Once there, leave the car behind: Cambridge is flat, well served by cycle paths, and small enough that an audio-guided walk from King's Parade to the Backs and over to Kettle's Yard fits comfortably into a single day. Check college opening hours before you go; some are free to enter, others charge or close during exams.