Riding to the top of Europe’s longest curved escalator takes well over four minutes. People around me make use of that time to snap selfies as we rise towards the public plaza within Hamburg’s new waterfront icon, the Elbphilharmonie.

The multi-purpose building also hosts a 2,100-seat concert hall, a 550-seat recital room, 85 luxury apartments, the Westin Hamburg Hotel plus an underground car park. Many of the visitors are locals, entering for the first time, and their excitement is palpable.

They’ve had to wait far longer than anticipated for the Elbphilharmonie to open. The project was supposed to be completed in 2010 but disputes pushed the timeline out to late 2016, causing costs to the city to soar to €789 million — around £660 million. There’s a popular joke here that more lawyers than construction workers earned a living from the Elbphilharmonie.

Strolling around the plaza’s viewing gallery are some of the best views over Hamburg’s skyline. Across the River Elbe sit the docks of Europe’s third largest port and the yellow façade of the Stage Theatre, which has hosted a German language production of The Lion King for the past 15 years. Musicals, theatre productions and its diverse nightlife have long made Hamburg a popular weekend destination and that domestic appeal is gradually becoming more international.

Though the city lies 68 miles inland from the North Sea, the river is navigable by both container vessels and oceangoing cruise ships — the Queen Mary 2 is a regular visitor.

As a result, architects Herzog and de Meuron were careful to eliminate potential disturbances from the noise of ships’ horns inside the Elbphilharmonie’s state-of-the-art concert hall, which seats all attendees within 30 metres of the conductor. Ingeniously, 362 steel springs isolate the shell of the hall from the rest of the building. The renowned acoustician Yasuhisa Toyota designed the 10,000 individually shaped gypsum-fibre panels that collectively form the white interior walls.

I take a seat just six rows back from the talented young conductor Krysztof Urbanski as he leads the NDR Elbphilharmonie Orchestra through Igor Stravinsky’s The Rite of Spring. The performance is part of the low-cost Konzerte für Hamburg (‘Concerts for Hamburg’) series that aims to broaden classical music’s appeal. There’s no need for formal attire, meaning I’ve come dressed in jeans and comfy boots, clothing that’s as suitable for one of the evening Beatles’ Tours that singer-songwriter Stefanie Hempel leads through the St Pauli district.

Her two-and-a-half hour walking tours feature stories about the Liverpudlian musicians’ residencies at clubs within the city’s red light area between 1960 and 1962. Those long sets helped hone the band’s stage presence and they were performing at the Star Club just 11 days before the release of their first hit, Please Please Me.

At various points, she unpacks her ukulele to sing Beatles hits, inviting guests to join in; feeling a touch shy about singing in public I clap instead.

Along the way, she explains how a group of Hamburg-based Existentialists, known as ‘the Exis’, became friends with the Liverpudlians and influenced their clothing and hairstyles. It was here that the band members first wore their famous mop-tops. We say our farewells at Beatlesplatz, where a monument depicts outlines of the Fab Four and Stuart Sutcliffe, the band’s bassist when they began playing in Hamburg.

I’m discovering that the city’s musical pedigree is both long and strong. Several record labels have bases in Hamburg, which invites both established and up-and-coming bands to perform on the open-air stages of the Spielbudenplatz and nearby clubs during the annual Reeperbahn Festival, from September 20 to 23 this year.

The city is “where music seems, as it were, to have its homeland” according to Georg Philipp Telemann, the Baroque composer, about whose life and work I learn in the recently established Composer’s Quarter, the home of six museums relating to classical music. Here, Stolpersteine, brass memorial plaques set into the pavement, name Jewish inhabitants of the Neustadt district who were deported and murdered during the Holocaust. Just steps away, the Gustav Mahler Museum and Fanny and Felix Mendelssohn Museum provide insights into cultural contributions by Jewish musicians.

The nearby Hamburg Museum holds a permanent exhibition about Jews in Hamburg, recreating the interior of the synagogue at Heinrich-Barth-Strasse from 1885. Informing visitors about religious rituals, it tells how Sephardi Jews arrived from Portugal in the 1580s. Those merchants were initially welcomed, because of their overseas trading connections, and helped establish a Jewish community that numbered 20,000 people at its peak, in 1925.

Seeing my interest in the life of Albert Ballin, the Jewish shipping magnate who was the chairman of the HAPAG shipping line at the turn of the last century, a fellow visitor asks me, “Have you visited the BallinStadt Emigration Museum?”

She explains that the museum replicates the halls from which five million people emigrated to the Americas. A significant proportion were Ashkenazi Jews fleeing pogroms and persecution in Russia and eastern Europe. “It’s the flipside of the story told at Ellis Island in New York,” she adds.

Though it sounds interesting, I already have plans to visit the Jewish Cemetery of Altona Königstrasse. Despite being just a couple of miles from where I’m standing, Altona was a separate municipality until 1937 and part of Denmark until the 1860s.

On Unesco’s list of tentative world heritage sites, it is the city’s oldest cemetery. The Sephardi part was established in 1611 while the oldest Ashkenazi burials date from 1616. Tagging on to one of the weekly tours of the historic site I hear how Allied air raids and systematic Nazi vandalism inflicted damage during the 1940s. Several headstones are now laid out horizontally. Others still bear intricate bas-relief sculptures, including the tree of life and animals, plus lengthy texts.

Whether it’s the city’s new developments or long heritage, culture seekers will find what they’ve been looking for.