Seven days in Belgium and Luxembourg: a capital that argues, and a capital on a cliff

Gilded baroque guild houses on three sides, a 15th century town hall with a 96 metre spire on the fourth, and a trade emblem carved on each front: the swan, the wolf, the boat. Most of it went up within five years of a French bombardment in 1695. Free, always open, and best floodlit.

A glass-vaulted arcade of 1847, older than the famous ones in Milan and Naples, and still full of chocolate makers, a bookshop and a cinema under an iron and glass roof. Two hundred metres, and worth walking even if you buy nothing.

Half a metre of bronze boy on a street corner, usually dressed, out of a municipal wardrobe of several hundred costumes changed for saints' days and state visits. He is much smaller than everyone expects and the city finds that funny.

A cafe unchanged since the 1920s: marble tables, long mirrors, waiters who have seen everything. The house gueuze is sour, dry and closer to cider than to beer, which is what Brussels drinks and what visitors are usually not ready for.

Avoid the restaurant alley one street off the square, where the menus have photographs on them. The fish restaurants around Sainte-Catherine and the kitchens at the Dansaert end are where the city eats.

Seven thousand instruments over four floors, inside the old England department store of 1899, black wrought iron and glass and one of the finest Art Nouveau buildings in the city. Infrared headphones play whatever case you stand in front of, and the top floor cafe has a free view over the rooftops.

The museum cafes are decent and the streets down towards the Sablon are better. Keep it to an hour; there are two more collections after it.

Six centuries of painting with the Flemish rooms at its heart: Bruegel the Elder, van der Weyden, Rubens, Jordaens. The old and modern buildings connect internally, so one ticket buys much more than an afternoon can absorb.

More than two hundred works by Magritte, hung in the order he made them, so the bowler hats and the pipes only arrive once you have watched him get there. Same entrance as the fine arts museums; ask for the combined ticket.

The last traditional lambic brewery in Brussels, working since 1900 and still a family business. Nothing is inoculated: the wort cools overnight in a shallow copper pan under the roof tiles and ferments on whatever wild yeast lives in the rafters. Self-guided, an hour, tasting included.

The only survivor of the seven gates of the second city wall, built in 1381 and spared because the 19th century made it a museum rather than rubble. Climb it for the wall walk and the view over the Marolles.

The old working quarter under the Palace of Justice keeps its junk shops, its cheap kitchens and a flea market on the Place du Jeu de Balle that runs every morning of the year and clears by lunchtime.

Victor Horta's own house and studio of 1898 in Saint-Gilles, kept as he built it down to the door handles, with a staircase under stained glass that is the reason it is on the UNESCO list. Timed tickets, no photography, and a long queue on wet Sundays.

A promenade along the old city wall with the whole Alzette gorge below it: rooftops, an abbey, bridges and the cliff the fortress was cut into. Somebody once called it the most beautiful balcony in Europe and nobody has argued since. Free, open always, and best in the last hour of light.

Tunnels, galleries and gun chambers cut into the rock under the Bock, where Count Sigefroy built the first castle in 963. The system once ran for 23 kilometres and could hide thousands of men with their kitchens and workshops. Steep steps, low ceilings, and holes in the cliff face with a view straight down.

The smaller of the two squares on the plateau and the one where the city sits outside, with a bandstand in the middle, cafe tables on all four sides and free concerts on summer evenings.

Prices here are a step up from Brussels and the cooking is generally worth it. Note where you ate and come back at lunchtime, when the same kitchens do a set menu for a fraction of the price.

The lower town at the bottom of the gorge, where the Alzette runs past old stone houses and locks with the fortifications on the cliff above. Lanes, footbridges and two or three of the best bars in the city. Going down takes fifteen minutes; coming back up is what the lifts are for.

A Benedictine abbey by the river that spent most of the 19th and 20th centuries as a prison and is now a cultural centre, with a courtyard, a cafe, concerts and exhibitions. Free to walk into, and the cliff behind it is worth the ten minutes on its own.

The Grund has good kitchens by the water. Kirchberg feeds thousands of office workers at midday and is cheaper than the address suggests.

Pei's museum of modern art, opened in 2006 in the surviving corner of an 18th century fort, with the old stone walls left standing around the new glass. The collection changes constantly and the building is half the visit. Ten minutes on the tram, and the tram is free.

One of the great feudal castles of Europe, built between the 11th and 14th centuries on the site of a Roman fort, ruined in the 19th century and rebuilt from the 1970s. Twenty rooms including a Romanesque chapel and a banqueting hall, and a walk up from the town steep enough that a shuttle exists for it.

The main street runs down to a bridge over the river and is lined with terraces. Nothing in Vianden is expensive by Luxembourg standards.

Victor Hugo spent part of his exile here, most notably three months in 1871, in a house on the bridge that is now a small museum of the rooms he used, the drawings he made of the ruined castle and the politics that put him there. Forty minutes, and the best thing in the town after the castle.

An old open chairlift that carries you out of the valley in eleven minutes to a terrace bar with the classic view of the castle on its ridge. It runs from spring to autumn and stops in winter and in bad weather.

The national collection, dug down into the rock over several floors: prehistory and Roman Luxembourg at the bottom, then coins, decorative arts and a strong fine art section on the way back up. Quiet on most mornings and free on Thursday evenings.

A Jesuit church begun in 1613 and made a cathedral in 1870, with a black marble crypt holding the grand ducal family and two bronze lions at the door. Outside stands the Golden Lady, a war memorial pulled down by the German occupiers in 1940 and re-erected in 1985 after the pieces turned up under a football stand.

The tram runs from the old town past the station and out towards the airport, and costs nothing. Twenty minutes to either, with no ticket to buy and nothing to validate.