Eight days in the Baltic capitals: three countries on one bus ticket, south to north

Vilnius Cathedral looks like a Greek temple because it was rebuilt as one: the first church here went up in 1251, burnt repeatedly, lost its south tower in 1769, and what stands now is a neoclassical reconstruction finished in 1801. Go in for the chapel of St Casimir, which survived from the earlier building and is Baroque at full pressure, black and white marble and silver relief. Outside, set into the paving of the square, look for the tile marked Stebuklas, the word for miracle: it marks the southern end of the human chain that ran from here to Tallinn in August 1989, which is the route you are about to travel.

Then climb the hill behind it. Gediminas Castle is the upper of three castles that stood here from the fourteenth century, reached by a cobbled path or a funicular from the courtyard below. The courtyard at the top is free, it stays open late, and the view is the old town on one side, the glass towers of new Vilnius across the river on the other, and three white crosses on the hill opposite. Come at sunset and let the flight wear off.

Vilnius University has been running since 1579 and its old campus is a warren of linked courtyards rather than a single building, with the Church of St Johns in the middle. Four of the courtyards and the church cost nothing to walk into, which very few visitors do, and there is a frescoed hall behind them worth asking about at the desk. Go early, while students are crossing it.

Work east to the river for St Anne's, a small flamboyant Gothic church of about 1500 built from thirty three different shapes of brick and essentially unaltered since. The story here is that Napoleon wanted to carry it back to Paris on the palm of his hand. Behind it, on the same lawn, the larger Bernardine church was part of the city defences and still has the loopholes in its walls.

Then walk the length of the old town, down Pilies and Didžioji and Aušros Vartų, which is the best single street in the Baltics, past the town hall and out to the Gate of Dawn. It is the last of nine city gates and there is a chapel over the arch holding an icon of the Virgin painted in the 1620s, one of the great pilgrimage sites of this part of Europe. You reach it through the church next door, up a staircase, following the headscarves. When the chapel windows are open, people stop in the street below and kneel on the cobbles where they are.

The building on the corner of Gedimino was the Gestapo headquarters and then the KGB's for fifty years, and the names of people killed in it are carved into the granite of the outside wall at pavement level. Inside, the offices and the basement are as they were found in 1991: the cells, the padded room, the water cell, and the execution chamber where over a thousand people were shot, now under a glass floor. Two hours, and it is not curated to soften anything.

The museum has one significant blind spot and it is worth knowing before you go in. Until 2018 it was called the Museum of Genocide Victims and dealt almost entirely with Lithuanians under Soviet rule; the murder of about a hundred and ninety thousand Lithuanian Jews, most of it in the first months of the German occupation, had a single basement cell. That is beginning to change and has not changed enough.

Cross the city and the Vilnia stream in the afternoon and the register changes completely. Užupis was the cheap flooded quarter behind the old town, and on 1 April 1997 the artists living there declared it an independent republic. It has a president, an anthem, an army of about a dozen, and a constitution on mirrored plaques in twenty odd languages, which grants the right to be unique, the right to be idle, the right to be misunderstood, and confirms that a dog has the right to be a dog. The bronze angel in the square went up on April Fools' Day 2002.

Walk up through the park behind it to Three Crosses Hill. Crosses have stood there since the early seventeenth century, were banned by the tsarist authorities in 1869, rebuilt in concrete in 1916, blown up and buried by the Soviets in 1950 and dug out and re-erected in 1989. The view over the old town at dusk is the one to finish Vilnius on.

Take a morning coach. Vilnius to Riga is two hundred and sixty odd kilometres up through flat farmland and pine forest with one border you will not notice, and it takes about four hours. Buy the ticket a few days ahead and take the earliest departure you can face, because it buys you a whole afternoon at the other end.

The bus sets you down at the market halls, five minutes from the old town. Walk in to the square the whole of Vecrīga is built around. The House of the Blackheads is the elaborate red brick and stone building with the stepped gable, and it belonged to a guild of unmarried foreign merchants. The original was fourteenth century and decorated for six hundred years; the Germans shelled it in 1941, the Soviets bulldozed the remains in 1948, and what you are looking at was rebuilt between 1995 and 1999 from photographs. Riga does not pretend otherwise.

Then take the lift up St Peter's, which is the thing to do on your first evening. The church dates to 1209, its spire has burnt, blown down and been shot off repeatedly, and the current one is a 1970s steel reconstruction with a lift inside. From the platform: the red roofs of the old town, the Daugava and its bridges, the hangars of the market, the Stalinist tower behind them, and the sea on a clear day. It does not run on Mondays.

Start at the Central Market, because it is next to where you arrived and because it opens early. The five vast halls are surplus German Zeppelin hangars, bought in 1920 and re-erected here, each now devoted to one thing: fish, meat, dairy, vegetables, bread. Hundreds of stalls stand outside under awnings. This is where Riga shops, prices are what Latvians pay, and the cafés wedged between the halls will give you a plate of hot food for a couple of euros. Buy smoked fish and black bread for the bus tomorrow.

Then the black box behind the main square. The Museum of the Occupation of Latvia covers 1940 to 1991: the first Soviet year, the deportations of June 1941 when fifteen thousand people were loaded onto trains in a single night, the German occupation and the destruction of Latvia's Jews, the return of the Soviets, and the forty five years that followed. It is long, densely written and the most important two hours in the city.

Give the afternoon to the reason Riga is on the World Heritage list. Walk out past the Freedom Monument, forty two metres of travertine and copper unveiled in 1935 and never taken down by the Soviets, though laying flowers at it was made an arrestable offence and people did it anyway. Cross Bastion Hill, the old rampart turned into a park with the city canal running through it, and keep going north east into the Quiet Centre. Alberta iela is the concentrated version: one short street of apartment blocks from 1901 to 1908, most by Mikhail Eisenstein, whose son Sergei made films, with screaming faces two floors up, sphinxes, peacocks and enormous stone heads. Walk it twice, once looking up and once looking at the doorways. Elizabetes and Strēlnieku carry more of it.

Riga to Tallinn is about two hundred and eighty kilometres and four and a half hours, along the coast road through Pärnu, with the Gulf of Riga appearing on the left for stretches of it. Again, take a morning bus.

You arrive at the Bussijaam, a couple of tram stops from the old town, and the change of country is immediate. Estonian is not a Baltic language at all; it belongs with Finnish, and after two countries of Latvian and Lithuanian the signs suddenly look like nothing you can guess at.

Come into the old town through Viru Gate, which is two round towers with conical roofs and a flower market underneath, all that is left of the fourteenth century east gate. Behind it is the lower town, the merchants' and artisans' half of medieval Tallinn as opposed to the hill where the bishop and the nobility lived, and it is the busiest part of the city by a long way. Five minutes in, Town Hall Square opens out, with the only surviving Gothic town hall in northern Europe on its south side, finished in 1404, and a weathervane of a medieval guard on the spire that the city uses as a mascot. The terraces round the square are priced accordingly; walk two streets off it for dinner.

Toompea is the limestone hill the town grew beneath, reached by two lanes called the Long Leg and the Short Leg, which were gated against each other because the hill and the town below were separate jurisdictions that did not always get on. Alexander Nevsky Cathedral is the first thing at the top, built between 1894 and 1900 during the Russification years and placed deliberately opposite the seat of government on the highest ground in the city. Independent Estonia debated demolishing it in 1928 as a monument to oppression, and lost the argument.

Across the square is the Toomkirik, six and a half centuries older and much quieter. Founded in 1229, Lutheran from 1561, it is the burial church of the Baltic German nobility, and the walls are covered floor to ceiling with the carved wooden arms of families who ran this country for seven hundred years and left in 1939. Climb the tower. Behind it, the Kohtuotsa and Patkuli platforms give you the photograph of the lower town roofs, and both are free.

Come down in the afternoon for Niguliste, St Nicholas's church, at the far end of the lower town. It was the German merchants' parish church, gutted by Soviet bombing in March 1944 and burnt again in the 1980s, and it was rebuilt as a museum rather than a working church. Inside is Bernt Notke's Dance of Death, painted in Lübeck in the late fifteenth century, in which a pope, an emperor, a cardinal and a king are led away by skeletons. Only the first seven and a half metres survive. It is the finest medieval painting anywhere on this coast and there is rarely a queue for it.

Walk north out of the walls for the last morning. Kalamaja is the oldest suburb of Tallinn, fourteenth century in origin, named for the fish houses that stood there, and it was a workers' district of one and two storey wooden apartment buildings, most of them thrown up around 1900 for factory hands. Nobody with money lived there for a century, which is exactly why it survived, and it is now the best part of the city to walk with no destination: painted timber facades, small front gardens, a linear park where the railway used to run, and the Telliskivi complex of old rail workshops full of bars, studios, a flea market and the restaurants Tallinn actually eats in.

Lennart Meri airport is four kilometres from the centre, which is closer than almost any capital in Europe, and tram 4 runs from the middle of town to the terminal door in about fifteen minutes. There is no need to leave early.