Budapest is best in the seasons of spring and summer, the guidebooks say, and probably they have a point. But a stout pair of winter walking boots can take you around the city on a route that will leave you better acquainted with its soul, and your own.

Business took me to the Hungarian capital city, and the lack of availability of an air ticket home to Sofia spared me a day free; a precious thing, time, to take the measure of the dimensions of a city. Travel on four continents has taught me that, along with the knowledge that doing it all on foot ushers you in to an insight better than a point-to-point by tour bus or underground metro train, the latter short-changing you with rushing views of dark concrete in exchange for boxes ticked.

Street map and sketchy notes in hand, my first stop was St Stephen’s Basilica, the first major landmark from my hotel. Gilded Latin script proclaims "I am the way, the truth and the life" in the stone, but from any point, it is the dome that hypnotises, looming 96m above ground level at St Istvan Square. For the souls of patriotic Hungarians and devout Roman Catholics, there is much holy about it, not least its most famous feature, the dessicated hand of St Stephen, who took his country into the Christian faith.

The cathedral’s history, however, is troubled. It went through a number of architects, is notorious for its dome having collapsed in 1868 and apart from a number of other fits and starts, was bombed out in World War 2. Whispers reached me locally that it is jinxed. Certainly, among places of worship (of various faiths) that I have visited as a traveller, it claimed a record as the one where I have lingered the least. Aesthetically magnificent, yet somehow the massive volume of gloomy air bears down oppressively. It was not just the season.

Purposefully down the nearby junction with Andrassy Avenue to the House of Terror (stay with me, this walking tour gets more cheerful later on), now in its ninth year as a complex combination of exhibits, text, video and specially-commissioned musical background to the terrors unleashed, respectively, by the fascist Arrow Cross regime during World War 2 and their communist successors, the latter finding the premises convenient enough to change the label on the front door and continue the routine of torture and executions inside.

I have been before to places where oppression lingers in the air: on the worst scale, the Nazis’ Sachsenhausen death camp in eastern Germany (the communists also restored that to use) to that other place that sought to crush the soul, Robben Island. The House of Terror is not a browsers’ museum; unlike most others, visitors must tour by a preset route, to the final drama of a descent to the basement where enemies of the state were put to death – a journey taken in a lift that darkens for the occasion for an agonisingly slow memoir of just how this was done.

Arguably a model for outrightly political museums, the place leaves one with, if nothing else, a certain relief at leaving, and a repeat of a vow to oneself to fight the evil when it rears its head.

Follow me down Andrassy, a walk that is long but worthwhile with tempting places to eat and drink along the way; yes there are the stairs down to the metro at regular intervals, and the tour buses splash past, but every sign on every house, shop window and (further down) embassy tells a vignette of a story.

Heroes Square, and the ascent of the stairs to the Museum of Fine Art and into a realm of upliftment. The ticket office, for which there is an understandably long and eager queue, offers options to tour the entire collection or selected parts of it, such as the temporary exhibition Botticelli to Titian (still on until mid-February 2010; the museum’s website szepmuveszeti.hu has details of other temporary exhibitions on and forthcoming). I took the glutton’s ticket, wanting to see everything, conveniently forgetting past incidents of exhaustion in galleries elsewhere.

I have mentioned the website, so I shall not type out the entire catalogue; space would not permit, given that the building, dating from the early 20th century, hosts about 100 000 items (Old Masters alone accounting for 3000 of that total). I followed my nose, and as an unreliable guide, relied on everything I have had close to half a century to learn about art. Tintoretto, Titian, Leonardo, on to Canaletto (Joy!), Van Dyck, El Greco, Rodin, Degas, Manet, Gauguin, Renoir, Poussin, Duerer… if I have left anyone out (I have), my apologies and I shall thank you individually after the speech. A happily hypnotised chicken, I left several hours later than I had intended.

It left me little time, after I had dodged the puddles and crossed a few roads (Budapest motorists have much better manners than their Sofia counterparts) to spend at the Szechenyi baths (szechenyibath.com). Its legend had gone before it; every Bulgarian friend who had made it to the Hungarian capital either in decades past or more recently had impressed on me that I should at least set my foot through the door to inspect the architecture and the interior.

That much I did, and instantly vowed to return when greater leisure is available. But by now the afternoon was outpacing me, and there was another walk ahead.

Its Hungarian name translated as Tobacco Street, and thus the Dohany Street Synagogue got its name. It is a neighbourhood that has seen soaring highs and plumbed the unimaginable depths; Theodor Herzl was born in a house there, and from 1854, the synagogue rose.

Its architecture and features are unusual; the architect, Ludwig Foerster, referenced Byzantine and Roman Catholic traditions; it is the first synagogue I have seen that boasts an organ, to say nothing of a pulpit that would not look out of place in a Roman church, even though it is topped by a Star of David.

A ticket buys you the opportunity to be frisked at security and offered one of the tours available in a range of languages. The large Spanish group embarked at the same time as the English one, which consisted solely of me, in the hands of a skilled guide. In the soaring magnificence of what is the second-largest synagogue in the world and the largest in Europe, I took my seat in a right-hand bench (my natural home given gender separation on normal days, while women go aloft to the upper level on High Holy Days).

The organ and other objections keep the Orthodox away; the community that worships here is active, for all that, and in spite of the Holocaust that brought the darker, evil times, when the Nazis and their allies encircled a ghetto next door, stabled horses in the synagogue, and based there, at one time, a German radio station and local Gestapo headquarters, the latter in the belief that the Allies would not bomb a synagogue.

Those times have passed, and on a memorial wall, I study the commemorative tablets (not those in Hungarian, beyond my comprehension) in Hebrew, Russian and English.

Outside, rain is falling on the memorial steel willow tree whose leaves bear the names of victims, and the monument to the Righteous who moved to help escapees, and the tombstones that otherwise, traditionally, would be nowhere near such precincts. In the souvenir shop (embossed mugs, yarmulkahs, menorahs and hannukias, as well as rabbi marionettes, no less), bright young girls emanate an indomitable spirit as they help me with the mysteries of purchases in forint.

An exhausted and happy stroll in the rain to the Christmas market and mulled wine, contemplation of the neon lights and strolling shoppers, and all that Budapest has shown me in just the few hours I walked just a few of its 525 square kilometres.