Even the most casual visitor to Vienna can’t help but be bombarded by the city’s Mozart-industrial complex.

Mozart’s face peers out from the wrappers of ubiquitous chocolate-­covered candies called Mozart Kugeln, grand cafes offer Mozart tortes, and souvenir shops sell Mozart keychains, stuffed Mozarts and even Mozart rubber duckies. Hawkers outside major sights aren’t pushing hop-on, hop-off bus tours but tickets to touristy concerts dominated by Strauss waltzes and, yes, the music of Mozart.

You can’t help but wonder: What about Beethoven?

Don’t get me wrong. I love Mozart, and it’s charming to see the city where he spent the last decade of his life celebrating him with so much kitsch. But Beethoven spent his last 35 years there, and it was in ­Vienna that he wrote or premiered most of his major works — including all nine symphonies — and changed many of our ideas about music, art and genius. Yet outside the loftier precincts of the city’s museums and concert halls, he is far less visible.

But why? Beethoven is one of the most-recognizable, most-performed composers in the world. His music, and the story of how he fought off despair as he lost his hearing and composed masterpiece after masterpiece, still inspires. But he could be a notoriously difficult man. And if the modern Mozart myth got a boost from the Oscar-winning 1984 film “Amadeus,” the Beethoven biopic that followed, “Immortal Beloved,” failed to ignite in the same way. The most successful recent Beethoven film? That comedy about a St. Bernard.

But this year the Beethoven story is being retold to a new generation. The 250th anniversary of his birth in 1770 is being celebrated all over the world: Concert halls are programming marathons of his music; museums are launching exhibitions; and new boxed sets of his complete works are being released by Warner Classics (on 80 CDs) and Deutsche Grammophon (on 118).

So the time seemed ripe for a pilgrimage in search of Beethoven, the man.

Starting out in the house in Bonn, Germany, where he was born to a family of downwardly mobile court musicians, I set out on a Beethoven odyssey, from the scenes of his upbringing to the places in and around Vienna where he lived and worked, despaired and triumphed.

I have to confess to some apprehension when I set out. I sometimes fear learning too much about my idols: No man is a hero to his valet, or to a rigorous biographer. And Beethoven could be extremely unpleasant. (Most troubling may be the bitter court battle that Beethoven, who never married, waged to wrest custody of his nephew from the boy’s mother; his nephew wound up attempting suicide.) Would facing his faults color how I hear his music?

There were certainly moments of TMI along the way: Some exhibits went so far as to describe Beethoven’s chronic diarrhea. But there were also moments of wonder: standing in the frescoed hall of the Viennese palace where his revolutionary Third Symphony, the “Eroica,” is believed to have had its first run-through and imagining how shocked those first listeners must have been.

Beethoven-mania in Bonn

It was only logical to start in Bonn, not only because he did, but because it is home to perhaps the best Beethoven museum: the Beethoven-Haus, his birthplace.

No one can accuse Bonn — a modest city on the Rhine that was improbably the capital of postwar West Germany before reunification returned the seat of government to Berlin — of overlooking its most famous native son. Even if his childhood there was unhappy.

You can hardly miss him, no matter how you arrive: Signs in Bonn’s train station proudly proclaim the city as his birthplace, and “BTHVN 2020” banners flutter along the roads. Souvenir stands sell Beethoven T-shirts. The imposing bronze Beethoven monument on the Munsterplatz, which Hungarian composer and pianist Franz Liszt helped pay for, remains one of the city’s defining images.

After checking into the modest-but-pleasant Hotel Beethoven (I’m an easy mark), I walked down the street to the Beethoven-Haus. There, in a cobbled inner courtyard, I found myself at the door of the vine-covered house where, in 1770, Beethoven was born into a prominent musical family that was about to fall into difficulties.

His grandfather, also named Ludwig van Beethoven, had been Bonn’s kapellmeister — an important post that placed him in charge of music at the court. But he died when Beethoven was 3. When Beethoven’s less-talented father, Johann, failed to win the post, he descended into alcoholism.

The museum, which was refurbished for the anniversary, is a fascinating musical reliquary: It displays the console of an organ that young Ludwig played as a child at early mass at a nearby church; the viola he played in the court orchestra; and his last grand piano.

Beethoven doesn’t wear glasses in his best-known portraits, so I was startled to see a pair of his spectacles — but I suppose people were as likely to take them off for oil paintings as they are for Instagram. Then there were the ear trumpets he used, hornlike metal devices that were created for him to stick in his ears by Johann Nepomuk Mälzel, an inventor who also made his metronomes.

I could not help but smile in the gift shop. It offered not only sober Beethoven busts, recordings and scholarly books and scores — but also Beethoven chocolates, Beethoven wines and, yes, Beethoven rubber duckies. Beethoven kitsch, at last!

A blockbuster exhibition running through April in the Bonn’s Bundeskunsthalle has gathered some of the world’s most important Beethoven artifacts under one roof, in ways that both illuminate and question Beethoven mythology.

Bonn’s historic center is its own Beethoven exhibit. In a church near his birthplace, I saw the marble-bottomed baptismal font in which baby Ludwig was baptized Dec. 17, 1770. Nearby, in what is now the university, I ducked into the Palace Church, where, as a child, he was assistant court organist. Then it was over to the market square, where Beethoven’s most influential early teacher, composer Christian Gottlob Neefe, discussed Enlightenment ideals with local intellectuals.

The grave of Beethoven’s mother, Maria Magdelena, in the city’s old cemetery, lies near the graves of composers Robert and Clara Schumann. She fell ill in 1787 while Beethoven, 16, was on his first trip to Vienna, where he had hoped to study with Mozart. He cut his trip short to return to her.

To understand how Beethoven finally got back to Vienna, I hopped on a train to Bad Godesberg, a former spa resort.

It was there, at La Redoute, an elegant ballroom, that Beethoven met Haydn in 1792 and showed him a cantata he had written. Haydn — then perhaps the greatest living composer, as Mozart had died the year before — agreed to teach him in Vienna.

It is not a museum, but when I ducked in, a man who worked there — these days it is used for weddings and events — gave me a look at the elegant blue-and-white neoclassical ballroom where they met.

When Beethoven left again for Vienna — this time, for good — his Bonn friends signed an autograph album for him. The entry by Count Waldstein, a patron, proved prophetic: “With the help of unceasing diligence you will receive the spirit of Mozart from the hands of Haydn.”

‘It was only my art that held me back’

There was never any doubt about where to start in Vienna: Heiligenstadt, which was still a wine-growing country village outside the city when Beethoven stayed there in 1802 and experienced one of the great crises of his life.

“O you men who think or say that I am malevolent, stubborn or misanthropic, how greatly do you wrong me,” he wrote there, in a soul-baring letter addressed to his brothers, and perhaps posterity, that came to be known as the Heiligenstadt Testament.

The letter, discovered after his death and presumably never sent, is the key to understanding his path from shame to despair to determination as he lost his hearing. Visiting the house where he wrote it, which is now a Beethoven museum, felt almost intrusive.

“Ah, how could I possibly admit an infirmity in the one sense which ought to be more perfect in me than in others,” he wrote, describing his “hot terror” of being discovered and his anguish at losing his hearing.

“Such incidents drove me almost to despair; a little more of that and I would have ended my life — it was only my art that held me back,” he wrote.

Heiligenstadt still feels like a country village, although it is now part of Vienna. I took a walk there along the Beethovengang, a wooded path like the ones he loved. Then I stopped at a rustic wine tavern where Beethoven had stayed, Mayer am Pfarrplatz, ordered a glass of blaufrankisch (a varietal of red wine) and pondered how, so soon after despairing, Beethoven entered one of his most groundbreaking periods.

Conquering a musical capital

It is still possible to visit the scenes of many of his Viennese triumphs.

At the ornate Lobkowitz Palace, once the home of a major patron and now the Theater Museum, I visited the Eroica Saal, where the first private rehearsals of his monumental “Eroica” Symphony were apparently held. In “Beethoven: Anguish and Triumph,” Jan Swafford described how the guests listened as “the players stumble through the strangest music any of them had ever heard.” A group of elementary school children filed in, sat on rainbow-colored mats, and began playing air piano to Beethoven.

At the Theater an der Wien, across the street from my hotel, another Hotel Beethoven (this one quite chic), Beethoven gave the premieres of his Fifth and Sixth symphonies — on the same night, during an epically long concert in 1808, which also saw the premieres of his Fourth Piano Concerto and his “Choral Fantasy.” The theater has since been rebuilt, but it was still thrilling to see where he was, literally, composer-in-residence — given an apartment by Emanuel Schikaneder, the impresario who built it and who had helped create “The Magic Flute” with Mozart and been its first Papageno.

I sneaked into the Austrian Academy of Sciences, which was under construction, to see where the premiere of his Seventh Symphony was held. My tour of the Austrian Parliament, to see where the Eighth was performed during the Congress of Vienna — in a ballroom in the Hofburg, the Grosser Redoutensaal — was less successful: The ballroom was rebuilt after a 1992 fire, its Imperial grandeur replaced by strikingly modern Josef Mikl paintings.

Finally, I made my way to the site where Beethoven died March 26, 1827, at 56. The building, on the Schwarzspanierstrasse, no longer stands, but two plaques mark the spot. After he died, visitors cut off his hair for keepsakes; strands still fetch thousands of dollars at auction. Mourners lined the streets for his funeral; it took nearly an hour and a half for the procession to reach the nearby Church of the Holy Trinity, where his funeral was held. It took me less than 10 minutes.

I walked to Beethoven’s first grave, in what was then Wahring cemetery, and where Schubert, who died soon afterward, was also buried. Both composers were moved in 1888 to the city’s ornate central cemetery, where they still lie beside one another, near Brahms’ grave. The Wahring cemetery is now Schubert Park.

Later, I stopped in the golden-domed Secession Museum to see Klimt’s phantasmagoric “Beethoven Frieze,” which he painted in 1902. It was a reminder of how Beethoven had inspired generations of very different artists.

So what did I get from the trip?

Yes, Beethoven could be unpleasant, sometimes cruel, and his politics defied easy categorization. His deterioration over the years was heartbreaking: A museum in a house he stayed at in the spa town of Baden described how a disheveled Beethoven had once gone for a walk and been arrested for vagrancy.

But any fears I had about delving too closely into his life, warts and all, were dispelled the night I heard the Vienna Symphony recreate the epic 1808 concert Beethoven had given at the Theater an der Wien.

Listening to his “Pastoral” Symphony that night, the bird calls he wrote for the woodwinds took me back to the bird songs I’d heard retracing his footsteps on the Beethovengang. Its rustic dance rhythms reminded me of Mayer am Pfarrplatz, the old wine tavern. The five-hour concert flew by.

Knowing more, I decided, made me appreciate him more, not less.