According to a new survey by TripAdvisor, Sheffield is the place to head this bank holiday weekend for the best-value UK city break. A three-night escape for two people costs an average of £706 – that's including hotel, sightseeing and meals – making it the cheapest in Britain. A break of the same calibre in London would cost £1,190 – more than double the cost of a long weekend in Sheffield.

But don’t go looking for typical tourist attractions. Although there are buildings of note, including the Grade II-listed Cutlers' Hall and 1893 Town Hall, there is no Princess Street equivalent; no souped-up riverside docks (as in Glasgow, Liverpool or Leeds) or cafe-strewn embankment (the Victoria Quays canal basin is of historical note only); no cutesy cobbled streets or soaring minster (like York) and alas, no castle (a casualty of the Civil War, Sheffield Castle was destroyed in 1648 to prevent it from falling into royalist hands.)

Although you don't have to look too hard to find Full Monty style pockets of deprivation, the city has seen serious aesthetic improvements of late. An impressive Winter Garden – the largest urban glass house in Europe – now faces Tudor Square, home to the Crucible and Lyceum theatres, and leads to the Millennium Galleries (the cutlery and silverware gallery is a highlight) where a partnership with the V&A has fleshed out the city’s cultural offering.

Fountains in Millennium Square Credit: AP

The Golden Route now provides a pleasant walking route from the smart railway station to the city centre.

The medieval Anglican cathedral, an astounding building to visit, has reopened following complete restoration and the site of the city's medieval castle is currently being cleared, with plans in place for an excavation of the site. The Sheffield Victorian Botanical Gardens have been entirely restored and remodelled and include a bear pit with, we have it on good authority, "a frightening model bear."

Over the decades, I’ve learnt to appreciate the city’s subtler qualities as only an outsider can. I’d wager the people are the friendliest you’ll find in any northern city. Not because they’re necessarily trying to be friendly, you understand, but because the locals’ utter lack of pretension – and how refreshing that is, too – precludes any form of rudeness, snobbery or pre-judgement.

"Sheffield is the sum of its parts. There’s no bucket list. Go and have fun" Credit: AP

Surveys reveal that it is voted the friendliest and safest city in the UK: Sheffield universities – there are two – have the highest retention rate for students and it was the only major city in the country not involved in the riots of 2011.

Humming nightlife, industrial heritage in spades and immediate access to one of the country’s finest national parks are among its selling points. A third of the city lies within the boundaries of the Peak District National Park, where the contrasting limestone dales and upland moors that give their name to the renowned Dark and White peaks are a short (cheap) bus ride away.

Travel via Loxley on the city’s outskirts and you’ll pass shimmering reservoirs and moody moors.

"A third of the city lies within the boundaries of the Peak District National Park" Credit: © Jon Sparks / Alamy Stock Photo/Jon Sparks / Alamy Stock Photo

Along with heritage woodlands and parks are green corridors reaching into the city itself. My earliest childhood memories include paddling in the babbling Wyming brook and jumping across its stepping stones in the Rivelin Valley. The Porter Valley recalls Hobbit country.

A clutch of excellent museums and visitor centres tell different aspects of the city's story. Abbeydale Industrial Hamlet and the Kelham Island (a man-made island in the River Don) Industrial Museum are musts; the latter includes the working colossal River Don steam engine.

At Porter Valley the city’s last surviving water-powered knife-grinding workshop features the restored Shepherd's Wheel.

A third of the city lies within the boundaries of the Peak District National Park... the dales and moors are a short (cheap) bus ride away

There are other little surprises around the city. The new visitor centre at Sheffield Manor Lodge, the Ruins of a Tudor manor house built in the great Sheffield deer park, tells the story of how Mary Queen of Scots spent much of her 14 years captivity in Sheffield as a "guest" of the grand Earl of Shrewsbury and his wife Bess of Hardwick.

Activities here should keep any family with a soupçon of inquisitiveness engaged. Ironically the lodge sits on the edge of the infamous and sprawling Manor – one of the city’s most notorious council estates.

But with urban grit comes creative edge. Sheffield’s contribution to the popular music scene needs little introduction. A blue plaque on Division Street (head here for non-chain bars) shows the spot where Jarvis Cocker once fell out of a window and broke his leg while trying to impress a girl at a party (the incident apparently inspired Common People).

"My earliest childhood memories include paddling in the babbling Wyming brook and jumping across its stepping stones in the Rivelin Valley" Credit: AP

Park Hill – a block of flats overlooking the railway station is name-checked in “Sheffield – Sex City” (the Pulp song which was in the encore at the band’s 2012 homecoming gig).

The Bowery pub at the junction of Division Street and Fitzwilliam Street is co-owned by former Arctic Monkeys bassist Andy Nicholson, who was at the official opening with Jon McClure (of Reverend and the Makers). Then there’s Hunters Bar, famously name-checked in an Arctic Monkeys lyric (He talks of San Francisco, he’s from Hunters Bar).

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Outside the Town Hall there’s the Hollywood-style Sheffield Legends Walk of Fame – “legends” include Def Leppard, Phil Oakey (of the Human League) Sean Bean, Jarvis Cocker, Seb Coe, Margaret Drabble and Jessica Ennis.

For a glimpse of Sheffield’s gritty industrial past, Sheffield-based Telegraph Travel contributor Stephen McClarence suggests a drink at the Fat Cat (thefatcat.co.uk), an award-winning Victorian corner pub in the regenerated cutlery-making area near the city centre. "It has a proper front parlour, no canned music and an array of real ales."

"Outside the Town Hall there’s the Hollywood-style Sheffield Legends Walk of Fame – 'legends' include Def Leppard, Sean Bean and Jessica Ennis" Credit: AP

If it's a gastro pub you're after McClarence recommends taking a taxi to the Cricket Inn (cricketinn.co.uk), "a smart gastro-pub down winding country lanes in the suburb of Totley serving satisfying British cooking." An Early Bird menu (Monday to Friday, 12 noon to 7pm) is priced at £12 for two courses or £15 for three.

At Christmas time some of the best examples of the West Gallery music revival can be found in the city’s festively decked pubs, where singing (pronounced sing-ging) rings out. “It was what people used to do before songs were hijacked by the church and became a more serious matter,” one local told me. “It’s great fun – I do it every year.”

In short, Sheffield is the sum of its parts. There’s no bucket list. Go and have fun. Take the kids; learn something. See some art. Get on a bus to the Peak District. And know that your pound is travelling further than it would in most UK cities.