Surely the most iconic landmark in Oxford, this grand circular library stands proud between the Bodleian Library and the University Church of St Mary the Virgin. It’s a beautiful example of neo-classical architecture, with a dome resembling a smaller version of St Peter’s Basilica in Rome. Visitors can’t go inside without booking a guided tour, but it’s hard to wander past without stopping to look up at the majestic 17th-century architecture. The Radcliffe Camera backs onto the main Bodleian Library, also well worth a stroll – its ancient courtyard is a delight.

A crown jewel in the city’s cultural offering is the Ashmolean – Britain’s first public museum – which is looking as good as new following a major revamp in 2009. As well as renowned collections of Egyptian mummies, Worcester porcelain and Pre-Raphaelite paintings, you’ll find a diverse calendar of temporary exhibitions on its top floor. Recent highlights include Jeff Koons, Young Rembrandt and Tokyo Art & Photography – a dazzling voyage through Japan’s vibrant art history.

This city of intellectual prowess is no less esteemed for its outdoor diversions. But before you end up falling off a punt on the Cherwell, or let the afternoon slide away with too many glasses of Pimm’s in the park, set aside some time to explore the Oxford Botanic Garden. The oldest of its kind in the UK, it houses floral borders, wild meadows and soaring greenhouses. An hour or two among the apple orchards, water lilies and soaring cacti will enliven your senses for the remainder of the afternoon’s cobblestones. Further afield, the Botanic Garden’s sister, Harcourt Arboretum, puts on a riotous autumn display. Pick up a handmade willow hamper at nearby Fallow and Fields to enjoy under its auburn canopies.

No summer’s day in Oxford is complete without hiring a punt – a shallow wooden boat driven and steered by a long pole – and wobbling your way down the Cherwell. They’re notoriously difficult to steer until you get the hang of it, but it’s a charming way to while away an afternoon. Pack a punnet of strawberries, a bottle of champagne and a wide-brimmed hat for full effect.

If you’ve already made it as far as Oxford, a brief flirtation with the Cotswolds is in order. Charming Woodstock, a 20-minute jaunt from the city centre, provides that perfect afternoon away – think tea rooms and boutiques, a bountiful Saturday farmers’ market and, of course, Blenheim Palace. Walks from Woodstock’s town centre afford generous views across glorious Lancelot “Capability” Brown-designed parkland, with the option to meander further and take in the Great Lake. Alternatively, head straight into the palace itself for an immersion in European baroque splendour, as well as, on occasion, contemporary exhibitions – previous editions have included Ai Weiwei and Cecily Brown. Refuel afterwards at Alfonso gelateria, back in town, which also does a seriously good hot chocolate, perfect for wintry days.

Small yet mighty, Modern Art Oxford is a sure highlight of any visit to Oxford. Showcasing both emerging and celebrated international talents, including Anish Kapoor, Marina Abramović and Ruth Asawa, the gallery’s temporary exhibitions programme is progressive and thought-provoking. There’s also a beautiful shop, featuring local design and craft. As one of its earliest visiting critics, back in the Sixties, Andrew Forge put it: Modern Art Oxford is “a place where things can happen… music can be played or children can run about, people can talk.”