Why go now?
A bizarre, beguiling blend of metropolis and market town, the Grand Duchy's compact capital is one of Europe's best-kept secrets. Though better known as a financial centre, it has a thriving cultural scene and its picturesque streets are never overrun by tourists.
Today, it celebrates its Fête Nationale, with a military parade and 101-cannon salute. And until September 15 it really comes alive with Al Fresco concerts, films and stage shows during the Summer in the City festival (summerinthecity.lu).
Get your bearings
Perched on a rocky plateau, protected by a deep ravine, the Grand Duchy's ancient capital has a breathtaking setting. The historic centre is encircled by the river Alzette and its tributary, the Pétrusse.
The modern districts of Gare and Bonnevoie are on the south side of the river, linked to the centre by several vertiginous bridges. Hidden in the river valley are the quaint old villages of Grund and Clausen. Kirchberg, to the north, used to be the site of the city's fortress; today it's the new cultural and commercial district.
Take a hike ...
... through the historic centre. Collect your sightseeing bumph from the helpful tourist office on Place Guillaume II, then cross the city's most handsome, historic square and into Rue du Marché aux Herbes.
Stop to admire the ornate Grand Ducal Palace – a 16th-century edifice and the first city hall. Walk right up to the main gates and gawp at the splendid sentries. If you're lucky, you might see the Grand Duke. Head right, downhill on Rue du St Esprit.
Take a view
Built on several steep hills, divided by perilous gorges, Luxembourg is full of stunning vistas. One of the best is from the terrace of the quirky Musée d'Histoire de la Ville de Luxembourg at 14 Rue du St-Esprit (mhvl.lu). The ride up to the terrace, in a glass lift, is a panoramic treat in itself.
The current exhibition, ABC Luxembourg (until March 31, 2013), explores the symbols and clichés associated with this enigmatic little nation. Open 10am to 6pm daily except Monday, Thursday to 8pm. Entry free on Thursdays 6-8pm.
Take a ride
From Rue du St-Esprit, cross the giddy viaduct, then stroll south past the chain stores of the lively, unpretentious Avenue de la Gare until you reach the train station.
For a "Do it Yourself" bus tour, board the No 16 (mobiliteit.lu), alight at Philharmonie, Luxembourg's beautiful modern concert hall at 1 Place de l'Europe (philharmonie.lu). The European Parliament is just across the road. Hop back on the bus as far as Royal to take you back into the centre.
Lunch on the run
Luxembourg is a city relatively free of sightseers, with lots of locals working in the heart of town, and it has plenty of good-value, good-quality lunch options. A La Soupe at 9 Rue Chimay (alasoupe.net) is a sleek, bustling café serving healthy stews and sandwiches. (Try their minestrone with white beans and parmesan.) It opens 7am to 8.30pm daily except Sunday.
La GrandRue is Luxembourg's smartest shopping street with lots of upscale designers, including Max Mara and Gérard Darel, as well as smaller boutiques. For chocolates, visit Namur at 27 Rue des Capucins (namur.lu). A Luxembourg institution since 1863, this chic confiseur is heaven for anyone with a sweet tooth.
Dining with the locals
In virtually any other European capital the Bistro de la Presse at 24 Rue de Marché aux Herbes (bistrodelapresse.lu) would be a tacky, overpriced tourist trap. Here in homely Luxembourg it's an unpretentious restaurant, serving hearty regional staples, with a bar propped up by convivial locals rather than camera-clicking sightseers. A vast, nourishing tureen of bouneschlupp (green bean soup with sausage) is great.
Go to church
Luxembourg's Notre Dame (cathedrale.lu) hardly qualifies as one of Europe's great cathedrals, but its modest proportions and humble ambience are part of its appeal. An odd melange of Gothic and Renaissance architecture, mainly built in the 17th century, it feels like a living, working church.
Out to brunch
Most eateries remain shut on Sunday mornings, but the café at Chocolate House, 20 Rue du Marché aux Herbes (chocobonn.lu), serves a continental breakfast of croissants, meat and cheese. Downstairs is the chocolatier, with all sorts of creations (try the chocolate chilli) to eat in or take away. It's open 10am-8pm Sunday, from 9am Saturdays and 8am on weekdays.
Luxembourg's cultural kingpin is the Musée d'Art Moderne at 3 Park Dräi Eechelen (mudam.lu; open Saturday to Monday 11am-6pm, to 8pm Wednesday to Friday).
Built within the ruined walls of an old fortress, it's not just a challenging forum, but an artwork in its own right. Designed by IM Pei, this graceful new building completes his "European Trilogy", alongside his Louvre extension in Paris and the German Historical Museum in Berlin.
More traditional tastes are met by the National Museum of History and Art on Marché-aux-Poissons (mnha.lu; 10am-6pm daily except Monday, to 8pm Thursday). The fine art includes works by Cézanne, Picasso and Magritte, but the highlight for British visitors is a pair of Turner watercolours depicting Luxembourg's old town and the dramatic landscape.
Icing on the cake
Luxembourg used to be one of the most fortified cities in Europe, and you can still walk along its ruined battlements. Start at the Bock Casemates, a labyrinth of tunnels built to withstand the fiercest siege, and follow the signposts for the Wenzel Path down the valley, across the river Alzette and through the Neumünster Abbey.
Follow the Pétrusse, the Alzette's tributary, along the leafy Vallée de la Pétrusse. The path rises into the city beneath the spectacular Adolphe bridge. The end of the Wenzel Path brings you to the pretty Municipal Park. The park's main landmark is Villa Vauban (villavauban.lu). This 19th-century mansion is now a smart art museum, currently hosting works by Dutch and Flemish masters.