You might have to scratch your head to think of something that Luxembourg is famous for. The Grand Duchy is the least populated of all the countries in the EU, and unless you’re a banker or a lawyer, it’s generally overlooked.

But the city has twice been the European Capital of Culture, and its UNESCO listed Old Town is utterly charming. You can walk the cobbled streets amongst medieval buildings, tour fortifications, wander in the parks, and sit for hours with a local beer, listening to live music on the street. Many of the people who work here disappear home to France or Belgium at the weekends, leaving central Luxembourg wonderfully quiet for visitors to explore.

Here are our top picks for the best things to see and do in Luxembourg:

1. Discover Luxembourg’s military

In Luxembourg, it’s all about castles and caves. This was once the most heavily fortified city in northern Europe, and though most of the fortifications were dismantled in the late 19th century, there are still plenty of sections to see.

The Bock Casemates is a natural defence, a rocky promontory that juts out from the Old Town. Count Siegfried built a castle on top of these cliffs in 963 and the underground passages and galleries survive. On a hot, summer’s day, the Bock remains cool, and the numerous archways in the rock beautifully frame the different city views. You can visit the Bock Casements on a self guided tour, or as part of a UNESCO Walk.

2. Explore the museums on MuseumSmile

Clearly visible across the gorge from the Casements are two remarkable museums whose architecture is completely juxtaposed. At the front is the Museum Drai Eechelen, what remains of a medieval fortress; and right next door is the striking glass pyramid of MUDAM, the Museum of Modern Art. They are part of Luxembourg’s Museum Smile – seven museums within a mile – and you can visit all of them for free with a Luxembourg Card.

3. Relax in the Grund

The Grund is the liveliest quarter of Luxembourg in the evenings, with and bars spilling out onto the medieval streets and squares. Liquid is right on the river, and it is without doubt the best option for craft beers: it has around 50 on any given day.

4. Shop ‘til you drop

Place Guillaume II is Luxembourg’s main square, and it’s been the centre of the city’s commercial life since medieval times. Come here on a Wednesday or Saturday to browse stalls in the lively market, which sell everything from artisanal cheeses and fresh flowers, to vintage clothes and bric a brac. You’re guaranteed to pick up some unique souvenirs.

5. Try some local Luxembourgish delicacies

On the northern side of Place Guillaume II are some attractive shopping arcades, and you can through to Kaempff Koeffler. This wonderful delicatessen is known for selling the best Luxembourgish produce, from chocolates and pastries, to cheeses and local. Whether you’re peckish and ready to pick up a picnic lunch, or shopping for gastronomic treats to bring home, this is the place to go.