Ten days in the Czech Republic: Prague, then east until the crowds stop

Start where the city has always started. Old Town Square has been the middle of Prague for a thousand years and carries the whole argument of the place in one open space: Gothic on one side, baroque on another, and a bronze reformer in the middle who was burned at the stake.

Wait for the clock on the hour. It is famously anticlimactic, everybody knows, and the crowd assembles anyway.

Then save the last hour of daylight for the bridge. At noon it is shoulder to shoulder; at dusk the crowd thins, the statues go black against the sky, and the castle comes up floodlit on the ridge ahead. Walk it slowly and eat on the far side.

The one morning on this trip where being early genuinely changes what you see. The castle grounds open at six and the buildings at nine. Arrive at opening and the cathedral is a room you can hear yourself think in; arrive at eleven and it is a queue that shuffles.

Take tram 22 up and work downhill. Buy the combined ticket at the information centre in the second courtyard rather than queuing separately for each building.

The complex is enormous, so do not try to see all of it: the cathedral, the lane of cottages along the north wall and one palace is a full and satisfying morning. Then leave by the eastern gate and come down the old castle steps for lunch.

Six streets in the north of the Old Town are what remains of one of the oldest Jewish communities in Europe, and they are the most affecting hours of any trip to Prague. The quarter itself was demolished and rebuilt around 1900 in the name of sanitation, which is why art nouveau apartment blocks now stand between the synagogues.

One ticket covers the sites and is sold at the entrance to any of them. Go at opening.

The cemetery is the part people remember. It is small, walled and completely full, because for centuries this was the only ground the community was permitted to use and the only way to keep burying was upwards.

In the afternoon walk south into the nineteenth century city, which is where the twentieth century actually happened and which the Gothic half can make you forget.

The hill south of the castle is the part of Prague that visitors skip, and it holds the two best rooms in the city. Take tram 22 to Pohořelec or the funicular from Újezd, and start at the top so that everything afterwards is downhill.

The monastery has been on this ridge since 1143. Its two library halls are the reason to come: one low and vaulted with baroque globes standing between the shelves, the other high, walnut to the ceiling and topped by a fresco of the history of thought. You look in from the doorways rather than walking about inside.

From there the ridge runs south through orchards to the tower, and the paths drop through the trees to the river. About an hour of walking, all of it downhill, ending where the crowds are, so time it for the late afternoon.

This is the last night in Prague. Eat well, and pack: the Brno train leaves from the main station in the morning.

Take a mid morning train and be in Brno for lunch. The line runs southeast across the Bohemian uplands and the change of scenery is gradual rather than dramatic, but by the time you get off, the beer has become wine and the prices have dropped by a third.

Brno hlavní nádraží is on the southern edge of the old town, five minutes from the cathedral hill. Drop your bag and walk up into a city that is doing nothing for your benefit whatsoever, which after four days in Prague is a relief.

The centre is a triangle of squares. Start in the largest, where the city installed an astronomical clock in 2010 that is a tall black granite column shaped like a bullet, tells the time in a way nobody can read, and is described by locals in terms that do not print well.

Finish on the cathedral hill for sunset, and listen for the bells at eleven the following morning: Petrov rings noon an hour early, and the story Brno tells about it goes back to the Swedish siege of 1645, when the besieging general is supposed to have said he would give up if the city had not fallen by midday.

The villa is the reason architects come to Brno. Mies van der Rohe built it in 1929 and 1930 for a young textile family who had eight years in it before the war took it from them, and what he did with a sloping site is still startling: you enter at the top, from the street, and the house opens downwards onto a single glazed living floor with a wall of onyx across the middle and windows that sink into the ground at the turn of a handle.

It is guided, it takes an hour, and you must have booked. Afterwards walk downhill to the café below, which is by another Brno modernist and has been serving coffee in the same room since the end of the 1920s.

Then take a tram across town and climb the other hill. Špilberk was a Moravian royal seat, then an Austrian fortress, then the prison the Habsburgs sent their political enemies to, and the casemates cut into the rock below it are the part that stays with you.

Eat in a wine cellar tonight. This is the country's wine half and it would be rude not to.

Twenty kilometres north of Brno the limestone gives way and a river disappears into it. On the surface there is forest and dry valley; underneath are more than a thousand known caves, five of them open to visitors, and a hole in the ground that is the deepest of its kind in the country.

Take an early train to Blansko and the shuttle from there, and book a morning cave tour if you are travelling in summer. The visit is on foot for the first half and then by boat through flooded galleries, and the water is cold enough that people who ignore the advice about a jacket regret it.

The tour surfaces at the bottom of the sinkhole, which is the moment worth coming for: a shaft of daylight a hundred and forty metres above you and trees growing on ledges up the walls. A cable car and a footpath take you back to the rim, where two platforms look straight down into it.

Be back in Brno by early evening. The valley restaurants are functional rather than good, and this is the last night in the city.

Ninety minutes northeast on the same line and the country changes again, from a working city to a small baroque one that has been quietly getting on with things since the seventeenth century. The station is a kilometre and a half from the old town and there is a tram outside the door.

Olomouc keeps its centre in two squares joined at a corner, and the first afternoon is simply walking them. The upper one is the size of a small park, with the town hall standing free in the middle.

The column in front of it is the reason the city has a UNESCO listing of its own. It went up over nearly forty years as a thank offering after a plague, and there is a chapel inside the base that opens occasionally.

Then round to the far side of the town hall for the clock, which is the strangest thing here. The fifteenth century original was destroyed in the last week of the war, and what replaced it in the 1950s is a mosaic of workers, chemists and athletes where the apostles used to be.

Fifteen minutes east of the square the town changes character completely. This is the ecclesiastical end: a cathedral, an archbishop's palace, a seminary and a Romanesque palace, all inside what was once a separate walled precinct.

Start with the palace, which is the oldest building in Olomouc and now holds the archdiocesan museum. Its Romanesque windows are still in the wall, carved and doubled, and the exposed stonework downstairs runs back to the twelfth century. This was the seat of the Přemyslid dukes, and the last king of that line was murdered in Olomouc in 1306, which ended the dynasty that had ruled the Czech lands since the ninth century.

The cathedral next door has been rebuilt so often that only the crypt gives away its age. Its south tower is the tallest in Moravia and the second tallest church tower in the country.

Keep the afternoon for the church that looks like nothing from the street and stops people in the doorway: three domes, stucco, gilt and a startling amount of light.

One last building. The big Gothic church by the market has an instrument that was the largest of its kind in this half of the continent when the organ builders finished it, and there is a festival around it every autumn. Climb the tower first; it is a short climb and the roofs of the whole centre are under it.

Before the train, eat the cheese. Olomoucké tvarůžky is made in a village thirty kilometres away, comes in small yellow discs, is almost fat free and smells like a serious mistake. Fried in batter it is very good. The locals will watch you try it and enjoy themselves.

Then the station, and either two hours back to Prague or an onward train east towards Kraków, which is a straightforward day's travel from here.