Inspired by the dreaming spires

One February evening in 1355, an Oxford student complain-ed about the quality of the wine in a city- centre tavern. The ensuing argument lit the touchpaper for a violent confrontation between town and gown that had been brewing for some time. The result was the terrible St Scholastica's Day massacre, which left 62 scholars dead. For centuries afterwards, the relationship between Oxford's academic fraternity and the rest of the city was uneasy, at best.

But in modern-day Oxford there are few signs of that bitter historical divide. In fact, the university and other places of learning are reaching out to the public as never before. You don't have to be a student at Oxford to gain access to the fruits of its learning.

The first institution to banish elitism was the Ashmolean Museum, the oldest purpose-built museum in Britain – and still Oxford's finest. When it opened in 1683, all and sundry were admitted to gape at its collection of specimens and curiosities from around the world. A German visitor in 1710 expressed surprise that the collection had remained intact, "since the people handle everything in the usual English fashion ... even the women are allowed up here ... they run here and there, grabbing everything."

None of this stopped the museum continuing to grow, and the latest phase in its development is underway: a £61m modernisation programme that will double the Ashmolean's gallery space, but will mean its complete closure from 1 January until the autumn of 2009. Parts of the museum are already cordoned off, but its stunning Western Art and Egyptian galleries will be unaffected until the turn of the year.

The beauty of Oxford is that most of its cultural and historical icons, as well as its colleges and spires, are confined to a relatively small area around the centre. Hiring a bicycle on the Cowley Road, I never needed more than five minutes to get from one venue to another, almost always in cycle lanes, and with barely a hill to slow me down.

After the man-made treasures of the Ashmolean, the next stop uncovered some astonishing finds from the world of nature. The Natural History Museum is a stately, neo-Gothic pile on Parks Road, where pride of place is given to a couple of scary-looking dinosaur skeletons. Nearby are the encased remains of one of the world's last dodos, the flightless bird from Mauritius that was extinct by the mid-17th century.

But the dodo still had an important part to play: it would make an appearance in Alice in Wonderland. Its author, Charles Lutwidge Dodgson (better known as Lewis Carroll), was a regular visitor in the 1860s. The Museum has caught the mood of the times by striving to make its collections more accessible to the public. Today, appointments can be made for private viewings with an expert.

On a sunny September day, even the dustiest academic needs fresh air and exercise, and Oxford offers both while continuing to stimulate the mind. Set back from the High Street, beside a leafy arm of the River Cherwell, the University's Botanic Garden is one of the city's beauty spots. The oldest physic garden in the country was founded in 1621 to explore the medicinal qualities of plants, at an exciting time when new discoveries such as the potato were arriving from the colonies. That work continues today: in one of a series of lectures this winter, Dr Jeff Aronson will explain "the history of the therapeutic use of the foxglove".

The garden's defining features are its original high walls, hardly altered since the 17th century, that support a more diverse array of plants than the Amazon Rainforest. While there, I was allowed to handle the largest seed in the world, the Coco de Mer, which takes about six years to grow larger than a rugby ball, and a lotus seed that germinated after lying dormant for 1,200 years.

About as many years ago, the Saxons built a defensive tower on a site west of the city centre, to which Oxford Castle was added in the 11th Century. By the time Oxford became the Royalist capital of England in 1642, the castle had become a notorious prison, and many Parliamentarians were imprisoned and died there during the Civil War. It housed prisoners until the 1980s, but is now being turned into the visitor attraction "Oxford castle unlocked".

An hour-long guided tour takes in the tower, with its fine panorama of the dreaming spires, the crypt (which is said to be jumping with ghostly presences) and the cells where a medieval miscreant had his ears cut off for nothing worse than possessing "a foul and saucy tongue".

My last stop is Broad Street, home of the bookworm and the scientist. On one side of the road, the Science Museum exhibits every imaginable kind of measuring instrument, with the English telescope in particular focus from 15 October, in an exhibition to mark its 400th anniversary. Downstairs, amongst Victorian cameras and gruesome medical equipment, a blackboard hangs on the wall containing the algebraic formulae chalked up by Einstein during an Oxford lecture in 1931, when he revealed how to measure the rate at which the universe was expanding.

Directly across the road, a fair proportion of the world's knowledge is gathered in a single place. The Norrington Room in Blackwell's bookshop contains three miles of shelving and 160,000 books – the most in a single room anywhere in the world.

And because every healthy mind needs rest and relaxation, it's entirely appropriate that Blackwells straddles one of the city's unsung seats of learning, the White Horse pub. Narrow, dark and intimate, the White Horse is an essential Oxford landmark on the road to enlightenment – but best not to complain about the quality of the wine.

TRAVELLER'S NOTES

Ashmolean Museum (Beaumont Street; 01865 278 000; www.ashmolean.org) open Tue-Sat (and Bank Holiday Mondays) 10am-5pm; Sun 12-5pm; admission free.

Natural History Museum (Parks Road; 01865 272 950; www.oum.ox.ac.uk) open daily 10am-5pm; admission free.

Oxford Botanic Garden (Rose Lane; 01865 286 690; www.botanic-garden.ox.ac.uk) open 9am-6pm, closing an hour earlier in winter. Admission £3, except on weekdays in winter, when there's no charge.

Oxford Castle Unlocked (Castle Street; 01865 260 666; www.oxfordcastleunlocked.co.uk) open daily 10am-4.20pm; tours cost £7.50 for adults; £5.35 for children under 15.

Museum of the History of Science (Broad Street; 01865 277 280; www.mhs.ox.ac.uk) open Tue-Fri 12-5pm; Sat 10am-5pm; Sun 2-5pm. Admission free.

Blackwells Bookshop (Broad Street; 01865 792 792; www.bookshop.blackwells.co.uk) open 9am-6pm Mon-Sat, Sun 11.30am-5.30pm.

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