Cambridge Market Square has been a place of trading since the Middle Ages, and it remains a good place to find everything from fresh food to second-hand bicycles. The Sunday market has a more arts-and-crafts feel, but you’ll still find good deals on local produce, too. Being fairly central and surrounded by cafés and restaurants, it’s a good place to get a refreshing start to your day and get a feel for the city.

Great St Mary’s Church is very beautiful both inside and out. Built in the 15th century, it’s worth taking the self-guided tour to see the two organs, the slightly bizarre pulpit on rails, and the impressive stained glass windows. However, it’s the tower which is especially famous. Added in 1608, it gives great views over Cambridge from the official centre of the city, with college buildings to the west and the city streets to the east. Access to the tower costs a small fee and you’ll need to climb 123 steps to get to the top.

The Fitzwilliam Museum is much like London’s British Museum. Not only is it free to enter and look around, but it houses a massive collection of antiquities from around the world inside a beautiful classical building. There are about half a million artworks, manuscripts, statues, coins, weapons – basically anything you can think of which has some historical value. The star attraction is sarcophagus lid of Ramesses III.

Quite far south of the city centre, but conveniently close to the train station, the Cambridge University Botanic Garden is a beautiful, peaceful place. A small admission fee will give you access to an impressive 40 acres of well-maintained grounds containing over 8,000 different plant species from around the world. There are several seasonal trails, helping you get the best out of your visit at any time of year, but it’s also nice just to wander along the winding paths. Check out the historical greenhouses to the north of the Main Lawn for flowers from the tropics, mountains, and deserts.

The deliciously gooey Chelsea buns of Fitzbillies are famous around the world and have been an iconic feature of this cake shop on Trumpington Street since it opened in the 1920s. Still showcasing its traditional style, the café also serves a good brunch and a very popular afternoon tea from 4pm. Being such a famous Cambridge institution, you can expect the store to be busy most days, but there is a smaller second branch on Bridge Street where you can get tasty sandwiches and, of course, those famous Chelsea buns.

Many of the colleges of Cambridge University back onto the River Cam, creating a view unimaginatively known as The Backs. Taking a punt – that most iconic of river transports in English university towns – is a great way to enjoy this view, which features many of the beautiful old buildings of King’s College, Trinity College, and St John’s College. Along the way, you can pass under the Mathematical Bridge (made entirely out of perfectly straight timbers) and the Bridge of Sighs, which has a similar design to the bridge it’s named after in Venice, Italy. Punts are available for rent at Quayside by Magdalene Bridge, among other places.

While the real name of this quaint old building is the Church of the Holy Sepulchre – named after the building of the same name in Jerusalem, which it was modelled on – it’s almost always known as The Round Church. There’s no prize for guessing why. First built around 1130, it’s among the oldest buildings in Cambridge and is one of the most iconic. Inside, the church is quite modestly decorated, but there is a small exhibition showing the impact of Christianity throughout history. Coincidentally, the church is surrounded by several excellent sweet shops.

Grand Arcade boasts more than 60 shops around a John Lewis department store, with a general trend towards high-street fashion and lifestyle brands. It has a bright and airy feel, for a 3-storey indoor mall, thanks to its glass roof and mostly white décor. Top brands include Calvin Klein, Laura Ashley, Ted Baker and many other mostly British designer labels. There’s also a good choice restaurants and coffee shops to choose from.

King’s College Chapel is one of the most famous and popular buildings in Cambridge. If you think the outside is impressive, you’ll be amazed by the interior, with its many beautiful stained glass windows, fan-vault ceiling, and historical artworks. As remarkable as the building is, the chapel choir is arguably even more famous. Attend the evensong service Monday – Saturday at 5.30pm or Sundays at 10.30am or 3.30pm to hear the world-renowned singers and their joyous hymns.

Cambridge is far from famous for its nightlife, but one particular pub deserves its place in history. What appears to be nothing more than a fairly large but typical English pub with a pleasant beer garden is actually the place where Francis Crick and James Watson announced that they had discovered the structure of DNA in 1953. There’s even a special ale available to commemorate the fact: Eagle’s DNA. You should also check out the RAF bar in the back, where you’ll find graffiti left by Second World War aircrews on the walls and ceilings (those must have been some wild parties!). For even more history, cross the road from The Eagle to St Bene’t’s Church – said to be the oldest building in Cambridge.