Every city worth its salt has a signature museum, filled to the brim with material culture from ages past. In London, it is the British Museum, New York has the Metropolitan Museum of Art and the Louvre has become an emblem of Paris.

The impressive Shanghai Museum is the equivalent in its home city. Rated first among 261 museums in Shanghai on TripAdvisor, this ding-shaped building – the 1990s design was influenced by the ancient bronze cook­ing vessel – is home to millennia of Chinese crafts­manship and, like its international counterparts, can be a slightly overwhelming experience. It remains, however, a must-see for admirers of Chinese art and history buffs.

But what of those 260 other museums? Armed with a metro card and an open mind, I embark on a quest to find some less obvious museums and galleries worth visiting while in the metropolis.

In a city filled with ostentatious architec­ture, it may come as a surprise to discover that one of the best museums in Shanghai is to be found in the basement of a nondescript residential compound in the former French Concession. Look out for a friendly guard – yes, they do exist in Shanghai – inside the complex, who will offer you a map to the right building. If you do manage to find your way to the Shanghai Propaganda Poster Art Centre (Room B-OC, 868 Huashan Road; shanghaipropagandaart.com), you’ll be re­warded with a visual history of 20th-cen­tury China related through hundreds of propa­gan­da posters, prints, graffiti and textiles.

The centre was born out of founder Yang Peiming’s private collection of propaganda posters, which he began amassing in 1995, when the state chose to remove and destroy such material. From brightly coloured Com­mu­nist slogans promoting an idealised view of a collectivised society to grand state­ments proclaiming China’s technologi­cal and military might and its affinity with Russian comrades, the paraphernalia at the museum offers a visceral glimpse into the efficacy and power of propaganda and mass marketing in the pre-digital age. Visitors can take home their very own piece of modern Chinese history – an original poster or an annotated copy of Mao Zedong’s “little red book” – from the centre’s shop.

Expect the unexpected when visiting the Power Station of Art (200 Huayuangang Road; powerstationofart.com), the first state-run museum for contemporary art.

The cavernous site was the Nanshi Power Plant before its transformation into the Pavilion of Future, for the 2010 Shanghai World Expo. Since 2012, the vast industrial space has been used to showcase pieces by emerging artists and collectives from around the world, many of which are provocative, setting it apart from the independent galleries in contemporary art district M50 and the private collections on display along the West Bund.

The LGBT guide to Shanghai - seven places to go in Pride week, and any time, to tap into social scene in China’s biggest city

The museum was a host venue for the 2016 Shanghai Biennale and current Power Station exhibits showcase the works of Polish graphic and poster artist Henryk Tomaszewski and prominent Indian archi­tect Balkrishna Doshi.

The Shanghai Urban Planning Exhibition Centre (100 Renmin Avenue; supec.org) might sound a little niche, but don’t be fooled – this is one of Shanghai’s best and most interactive museums. The remark­able evolution of the city from small port to thriving international metropolis is related through models, photography and multi­media displays. Transport, historic environ­ment and geology are among the subjects of several wide-ranging exhibits.

The ‘new Barcelona’: Shanghai, Korea tipped to be top holiday draws by 2035

The museum’s highlight – and the reason most people visit – is the large-scale model of the city on the third floor. Around the edge of the exhibit, local children point while searching for their homes in miniature as I try my best to get my bearings in the diminutive districts of Shanghai.

Worth a miss is the 1930s Old Shanghai reconstruction in the basement, a neglected addition to the museum that is in dire need of refurbishment if it is to achieve its goal: recreating the glamour of Shanghai in its heyday, as the Paris of the East.

In Hongkou district, the Shanghai Jewish Refugees Museum (62 Changyang Road) commemorates the city’s taking in of more than 20,000 escapees from the Holocaust in Europe before and during the second world war. Dr Ho Fengshan, “the Chinese Schindler”, provided refuge to many Austrian Jews while consul general of the Chinese consulate in Vienna from 1938 to 1940, granting thousands of special visas that allowed Jews to leave Austria. They could then enter Shanghai, an open port with no immigration controls.

My 48 hours in Shanghai

Housed within the beautifully restored site of the former Ohel Moshe Synagogue, the museum brings to life many poignant stories through a range of media, including video interviews, photographs and letters.

The synagogue, built by Russian Ashkenazi Jews in 1927, would became the centre of Shanghai’s Jewish ghetto in the 1940s, with tens of thousands of refugees sharing an area of one square mile with an estimated 100,000 Shanghainese. Little other evidence of the ghetto has survived the demolition and gentrification of Hongkou.

Another worthwhile attraction in the district is the Shanghai Postal Museum (395 Tiantong Road; shpost.com.cn). Located inside the spectacular 1920s China Post headquarters, the architecture and decora­tive motifs inside the building alone are enough to justify a visit. The museum details the development of China’s postal service, from humble beginnings – think messages scrawled onto tortoise shells dating back to the Shang dynasty (late 1500s BC-1046BC) – to an expansive network of pony express riders in the 19th century. A recently retired letter-sorting machine represents the postal service of more modern times.

A stamp collection may not sound like the most riveting of exhibits, but that in the Postal Museum acts as a thumbnail-sized illustrated history of events that have helped shape the People’s Republic. Look out for the colourful miniature depictions of collect­ivisation and the Great Leap Forward, especially if you haven’t yet made it to the Propaganda Poster Art Centre. Another high­light is the post office’s former mail-transit area, now a glass-covered courtyard show­casing vintage railway and horse-drawn mail carriages, best enjoyed on a sunny day.

In case you need further incentives to visit, the Postal Museum is free to enter, and just a short stroll from the bars and restaurants of the Bund. It’s open only on Wednesdays, Thursdays, Saturdays and Sundays, though, so don’t get caught out.