Eight days in the Low Countries: a canal city, a rebuilt one and a port that never stopped

Begun in 1648 as the city hall of a republic that had just become the richest state in Europe, and only turned into a palace when Napoleon's brother moved in in 1808. The Citizens' Hall inside has the whole known world inlaid in marble across the floor.

Next door to the palace, no longer a working parish church but the place where Dutch monarchs are inaugurated, most recently in 2013. It now runs exhibitions, so what is inside depends entirely on when you come.

A late medieval courtyard of houses built for beguines, lay religious women who took no permanent vows, and still lived in today. Number 34 dates from about 1420 and is one of only two wooden houses left in the centre. Go in quietly; it is somebody's front garden.

The grid of small streets across the canals west of the palace is full of small kitchens and no chains. Dutch restaurants stop serving early, so aim to sit down by half past seven.

Eight hundred years of Dutch art in a building worth the ticket by itself. The Gallery of Honour runs through Hals, Steen and Vermeer to The Night Watch of 1642 at the end, a militia group portrait so large it was trimmed in 1715 to fit between two doors.

Two streets east of the museums the prices halve. The Pijp is where the city eats: Surinamese, Turkish, Indonesian, and a lot of it standing up.

About two hundred paintings and five hundred drawings, hung in order so you watch the colour change from Dutch brown to southern French yellow over two floors. Timed tickets, online only, and the last slot of the day is the quietest.

The city's main park, five minutes west of the museums, with an open air theatre in summer and half of Amsterdam on the grass the moment the sun appears. Walk the length of it rather than sitting at the near end.

The canal house where eight people hid for just over two years behind a hinged bookcase. It is kept bare on purpose: no furniture, the original diary in a case, and the rooms as they were found. About an hour, and nobody says much on the way out.

Built between 1620 and 1631 and at 85 metres still the tallest church tower in Amsterdam, with the imperial crown of Maximilian on top. Rembrandt is buried inside in an unmarked grave whose location was lost. The tower is climbed by guided tour only.

The streets north of the Westerkerk are full of brown cafes doing proper lunches at ordinary prices, most of them with three tables on the pavement.

The largest street market in the country, running the length of a street in De Pijp six days a week: cheese, fish, fabric, and stroopwafels pressed while you wait. Best before eleven or after four.

Forty minutes on the intercity, every fifteen minutes, or twenty six on the fast international service if the timing suits. No reservation, tap in and out with a card.

A food hall of 2014 built inside a horseshoe of flats, so the arch over your head is somebody's living room floor and the ceiling is a painted mural eleven thousand square metres across. Ninety-odd stalls under it, and the medieval foundations found during construction are displayed in the basement.

Thirty-eight yellow cubes tilted onto a corner and set on hexagonal stalks over the road, built by Piet Blom in 1984 as an experiment in stacking houses like trees. People live in them; one is open as a show house so you can find out what a room with no vertical wall feels like.

The oldest harbour in the city, dug in the fourteenth century and one of the few corners the 1940 bombing left, now ringed with terraces and old inland ships tied up along the quay. The white office block on the corner was the tallest in Europe when it went up in 1898.

A small bar on the Witte de Withstraat that has been voted the best in the country more than once and functions as the start of most Rotterdam evenings. The whole street is bars and small galleries.

A cable-stayed bridge of 1996 with a 139 metre pylon bent like a swan's neck, and a bascule section at the south end that still lifts for shipping. Walk it south for the skyline behind you and the Kop van Zuid towers in front.

An observation tower put up for a horticultural exhibition in 1960 and extended in 1970 to 185 metres, with a rotating glass pod that climbs the top third of it. The view takes in the whole port stretching thirty kilometres west to the sea, which is the only way to grasp how big it is.

Between the tower and Delfshaven, the park has cafes attached to the galleries and a lawn to eat on. The main art museum here is shut for a long rebuild, so do not plan around it.

A church founded in 1417 in the one district the bombing missed, and the building the Pilgrim Fathers prayed in before boarding the Speedwell for Southampton in July 1620. The harbour outside is cobbled, quiet and full of old barges.

About forty minutes on the fast international service or an hour and a half on the ordinary intercity via Roosendaal, which costs a fraction as much. Buy an international ticket either way.

The largest Gothic church in the Low Countries, begun in 1352 and never finished: one tower reaches 123 metres, the other stops at the roofline and was abandoned. Inside are four Rubens altarpieces including the Raising and the Descent from the Cross, back in the building they were commissioned for.

The Grote Markt, ringed with tall stepped-gable guild houses and a Renaissance city hall of 1564, with a fountain in the middle of a soldier throwing a giant's severed hand into the river. That is where the name of the city is supposed to come from.

A medieval alley behind unmarked doors off the Oude Koornmarkt, opening into a chain of tiny courtyards with restaurants in them. Almost nobody who has not been told finds it, and it is thirty seconds from the cathedral.

A back-street bar with several hundred beers on the list and a cellar of bottles aged for years, some of them decades. There is no music, the owners will tell you what to drink, and it keeps its own hours.

The house and workshop of Christophe Plantin, the sixteenth century printer who produced the multilingual Bible that made his name, kept intact by his descendants until 1876. Two of the oldest working printing presses in the world stand in the back room, and the library and the courtyard are as good as the machinery.

The square outside the museum has a Friday auction and the streets around it have small kitchens doing lunch for people who work nearby rather than for visitors.

In the old Red Star Line sheds where two million people were checked, washed and inspected before boarding for New York between 1873 and 1934. It follows individual passengers rather than statistics, and one of them was Irving Berlin's family.

A ten-storey stack of red sandstone and wavy glass in the docks, opened in 2011, telling the story of Antwerp's trade with the world. The escalators up the outside and the rooftop terrace are free even without a ticket, and the view over the port at dusk is the reason to time it late.

A Jesuit church of 1621 with a plain grey exterior and an interior of marble, gilding and painted ceilings that Rubens worked on directly. The ceiling paintings he made for it burned in 1718; the Lady Chapel and the facade are his and survived.

Direct to Brussels Airport in about forty minutes, to Amsterdam in under two hours on the fast service, and to Paris in a little over two. Buy at the machine on the concourse.